Types of error correction

Students shouldn’t be afraid of using the wrong tense or omitting an article as making mistakes is the proof of learning, but the question is how teachers handle these mistakes. Too much error-correction can demotivate students, on the other hand, to let the conversation flow and not to correct any mistakes can also cause some problems in the future. The difficulty, of course, is in finding the middle ground. What should we correct, when should we correct it, and how should it be corrected?

Step 1 — Identify the reason for making mistakes (what to correct):

1. L1 interference — happens when the learner’s mother tongue affects performance in the target language. For example, learners make grammatical mistakes because they apply the same grammatical patterns as in their L1.
Read more in “Learner English”, a practical reference guide which compares the relevant features of a student’s own language with English, helping teachers to predict and understand the problems their students have. It has chapters focusing on major problems of pronunciation, grammar, vocabulary and other errors.
2. A developmental error — an error that occurs as a natural part of the learning process when a learner tries to say something that is above their level of language.
3. Overgeneralization of a rule — the process of extending the application of a rule to items that are excluded from it in the language norm.
4. A fossilized error — the process in which incorrect language becomes a habit and cannot easily be corrected.
5. A slip — a mistake made by a learner because they are not attentive or tired.
6. The nature of English — some set collocations, idiomatic expressions may cause errors.
7. Bad model — students learnt poor example and incorrect language from any available resources.

Some tips:

• We shouldn’t correct slips as they happen not because students don’t know the material but are caused by tiredness, inattention or just having too much to think about at the time.
• We should be careful with correcting developmental errors. Making such errors is a natural part of learning a language. You may just ignore them, as the student hasn’t studied the essential material yet or you can just articulate the correct sentence and that you are going to study that grammar or vocabulary later.
• We must correct all other types of mistakes, but don’t try to correct all the mistakes students make, choose ones which are relevant to the lesson/topic/activity.  

Step 2 — Choose the best time to correct (when)

There are two kinds of error correction:

1. Hot correction — as soon as we notice a student making an error.  
2. Cold correction (delayed error correction) — in order not to interrupt the learner during a speaking activity- as we are focusing more on oral fluency, we need to monitor and record the language of the learner to focus on the errors when the activity is complete. Conduct an error correction after the activity of at the end of the lesson.

Some tips:

• Use hot error correction during the presentation of the target language or controlled practice, as we are more focused on accuracy here. You should encourage SELF CORRECTION n first and then peer correction if needed, therefore ask CCQs (concept checking questions) that focus on meaning and form.
• Use cold (delayed) error correction while students are doing freer activity. Monitor the students and take notes of mistakes.

Step 3 — Choose an error correction technique (how)

There are many ways to correct errors:

Non verbal:

1. Finger correction — use fingers to show the mistake in the sentence.

2. Gestures — every teacher has a set of gestures to show students they’ve made a mistake. Teachers might gesture backwards with their hands to show students they haven’t used the verb in the past. Students often use the wrong pronouns, for example “She walked your dog.” You can point to yourself with a look of shock or surprise.

3. Facial expressions — when a student makes a mistake you can use an exaggerated facial expression to signal the mistake.
4. Cards (visual reminders) — some students often omit “-s”, “be”, etc. So you can just prepare a card with a big “S” or “AM/IS/ARE” and raise it every time students do this mistake, students instantly know they should go back and say it again. Later, you can just stick an empty card on the desk and point at it when necessary.
5. Visual analysis — write the sentence on the board and highlight indicators, question marks, everything that might help the student to correct the mistake, e.g.:

Verbal:

6. Repeat up to the error — repeat the whole sentence up to the error and make a pause waiting for the student to say the correct word/phrase. If the student has a difficulty correcting the mistake, give options.

S: My mum is really interesting in politics.

T: Your mum is really …

S: Interesting.

T: InterestING or interestED?

7. Demonstrate more examples — elicit or demonstrate more sentences with the same vocabulary or constructions.

S: I love SHocolate.

T: Read the words “chair, chicken”, now read this word “CHocolate”

8. Echoing — echo the mistake with emphasis on the mistake.

S: He like listening to rock music.

T: He LIKE?

S: He likeS listening to rock music.

9. Ask for clarification — ask your student to repeat the sentence.

S: I went to the magazine.

T: Sorry? Where did you go?

10. Recast — reformulate the utterance into a correct version (emphasising the place of the mistake) and encourage to continue the conversation.

S: Yesterday I went in the shop.

T: Oh really, you went TO shop. Which shop?

!!Try to elicit the corrections as much as possible. Get students to fix their own mistakes.

What error correction techniques do you prefer?

In English language teaching, error correction is something which is expected of teachers, so what error correction techniques are there to make the most out of the errors we correct? And how can we make sure that correction is helping our students?

As teachers, we are told that error correction is necessary. However, the value of error correction has long been discussed. Is what we are doing enough or should we stop altogether? In our post-method, eclectic, throw-everything-at-them-and-something-is-bound-to-stick era we need to be aware of the options available so we can decide what is best for us and our students.

Maybe you’re right, maybe you’re wrong

Expert opinions on error correction have evolved over the years. Take a look at these quotes and consider which one most closely represents your personal opinion.

• Like sin, error is to be avoided and its influence overcome, but its presence is to be expected – Brooks (1960)
• Error correction is a serious mistake because it puts students on the defensive and causes them to avoid complex constructions – Krashen (1982)
• You should tell students they are making mistakes, insist on accuracy and ask for repetition – Harmer (1983)
• There is a place for correction, but we should not overestimate it – Ur (1996)
• Feedback on learners’ performance in an instructional environment presents an opportunity for learning to take place – Larsen-Freeman (2003)
• Correction works best when done in context at the time the learner makes the error – Mackay (2007)

From error being seen as sin during the height of audiolingualism to viewing error as opportunity to learn, errors and correction have been a hotly debated topic in the ELT world.

This is why there is such a challenge for teachers. We must withdraw ourselves from our opinions and expectations in order to evaluate students on an individual level when it comes to errors. We then have to balance this with an institutional and cultural expectation to be corrected in the classroom.

Importantly, we have to ensure the learner has understood the correction, internalised it and improved their personal language system or interlanguage.

Interlanguage is a concept that refers to each learner’s personal knowledge of a 2nd language. It is the language which they know as they have learned it with potential for influence from their 1st language and overgeneralization of certain rules learned about their 2nd language. Hence the potential for error.

A learner’s interlanguage is unique to them. It is all they are able to use to communicate and it is what, as teachers, we are aiming to improve in each class, even in each interaction we have with students.

What is an error?

In ELT there have traditionally been two categories, errors and slips.

Errors happen when a learner doesn’t have sufficient knowledge of the language. This could occur when they have never been exposed the language and make an error because they have no prior knowledge to refer to. These are known as attempts. Or errors could come from the language having been acquired incorrectly and as far as they are concerned they are correct. These are fossilized errors.

Slips are the opposite end of the error spectrum. Slips happen when a learner knows the language but due to the speed of conversation or other factors, they say or write something incorrect. These are often self-corrected or ignored. They even happen to native speakers when we mispronounce a word or mix up words in an idiom that we’ve used a million times. One interesting thing to note is that even at the highest bands of C2 level, Cambridge writing scales say that inaccuracies that occur as slips are perfectly acceptable. They are not something to be punished.

Personally, I think there a bit of a gap here. We need something to fill in the middle ground. That is what I refer to as mistakes. Mistakes happen when a learner forgets the language that they have already acquired. It’s not that they don’t have the language, it’s that they haven’t accessed it correctly. Typical mistakes would come from L1 influence and often involve the use of false cognates or word order. The over-application of L1 rules in L2 frequently causes mistakes. This could happen to native speakers too, especially children. The typical example is when they conjugate an irregular past verb incorrectly (e.g. teached) because they have learnt a new rule and they start applying it too much.

When should we correct?

Correcting errors

Errors are the most difficult to correct, because not only are you providing a correction, you are also providing the knowledge necessary to fill the student’s gap in understanding. Errors should always be corrected, however, you need to be very careful about when and how to correct them.

We’ve all been in the situation where we try to correct an error quickly, only to get pulled down a rabbit hole where before we know it the board is covered in example sentences, phonemes and an explanation of the present perfect continuous. So correction of errors has to be structured and formulated in a way that allows students to recognise how to form the correct language, but without breaking the flow of the class.

Correcting mistakes

Mistakes should be dealt with completely differently. Mistakes are not due to lack of knowledge. Therefore, if you delay correction, the student will look at the error and instantly know what the problem is. They will think something along the lines of “Oh yeah, I knew that”. So what have we achieved as a teacher at that point? We haven’t helped to fill any gaps in knowledge.

That’s why mistakes should be corrected the moment they are made, even during a fluency activity. If you correctly identified the problem as a mistake, not an error, the correction should be quick and easy.

Correcting slips

Slips don’t need to be corrected at all. Slips are like your mother always confusing you and your sibling’s names. You know that she knows who you are, she just can’t ever seem to get it right. Correcting your mother may be satisfying for you as the corrector, but it’s not going to help her understand better who you are. And it might just make her flustered.

Correction in exam preparation classes

This is a blog about exam preparation after all. In many ways, everything that applies to error correction in general also applies to exam preparation classes. However, if anything, correction is even more important and even more expected. In general, we want our students to achieve successful communication and be intelligible. Unfortunately, for exams, this is often not enough.

The burden of correction falls even harder on the exam teacher. Insist on accuracy and demand the most of your students. They will thank you for it in the end.

Error correction techniques

There are many different types of error correction. Some of these we are taught how to do, while some of them come naturally. Some of them we would use in normal everyday situations.

Have you ever been in a shop and someone walks up to you to ask you where something is because they think you work there? How would you correct that person? You would probably say “I don’t work here” and for some reason apologise for their mistake. What you wouldn’t do is launch into a long explanation of why you choose to be an English teacher, not a shop assistant. And you wouldn’t start miming confusion and pointing across the shop to the employees who do work there.

That’s because certain correction techniques work better in some situations than others. Some work better for one type of error than for another. As teachers in the post-method era, we need to have an extensive bank of error correction techniques that we can dip into whenever we feel it’s necessary.

That’s our responsibility as teachers, to have the knowledge to be able to employ different techniques in different contexts.

Classic error correction techniques

Metalinguistic explanation S – She has a long black hair. T – Hair is an uncountable noun so it doesn’t take the indefinite article.

Repetition S – In the morning, I get up at seven o’clock, clean my tooth, have breakfast and go to work. T – You clean your tooth?

Direct explicit correction S – It is dangerous to smoke while you become pregnant. T – While you become pregnant is very different. You mean while you are pregnant.

Peer correction During an in class written activity where students complete a letter in pairs: S1 – Feel free to contact me if you are a problem. S2 – I think it’s have a problem.

Delayed correction S – The cheerleaders threw up high into the air. T writes the sentence down in a notebook and puts it up on the board after the activity. The whole group corrects the sentence.

Recast S – When we won, I was so exciting. T – You were excited.

Paralinguistic explanation S – Last night, while I was eating dinner, I started /dʒəʊkɪŋ/ so my friend hit me. T – Makes a facial expression of confusion. Mimes laughing and choking.

Elicitation S – Waiter, could you bring me some tissues, please? T – Could you bring me some ……, please?

Clarification request S – You can’t sleep in my room because it is too crowded, but you can sleep with my sister. T – Excuse me?

Tell them they are wrong Teacher hands out a worksheet S – I hope this the last /ʃɪt/ for today. T – That’s not how you pronounce that word.

Any and all of these correction techniques are acceptable and recommendable in the classroom. However, it is your role as a teacher to choose the best form of correction for the moment you correct.

Studies have shown, for example, that recasts, despite being the most common form of correction, are often overlooked. Students don’t notice they are being corrected. This happened more often with groups of Italian students than it did with groups of Japanese students. That’s because Japanese students have a significantly different mentality towards learning languages and were more attuned to the recast being an opportunity to learn.

Similarly, some students may like having their errors highlighted and displayed on the board after an activity while for others this could cause substantial embarrassment, thus lowering their motivation and causing them to avoid complex language in future interactions in order to avoid error in the future.

This is why we have to have a bag of tricks when it comes to error correction. There is no one-size-fits-all solution.

Adapted error correction techniques

While all of the above techniques are useful and acceptable depending on the context and circumstances, there is definitely a way to make error correction more interesting and ensure you are improving your students’ interlanguage.

Here are a couple of ideas that I have found to be effective:

Post-it correction

Method:

• Write errors on post-its or small
  pieces of paper.
• Slip those papers to the pair or
  group when they are done with the activity.
• They work together to write
  corrections on the same paper.

Benefits:

• Students are correcting their own
  errors rather than the smartest student in the group correcting everyone’s
  errors.
• Great for fast finishers.
• Post-its are fun.

Error collection

Method:

• Keep a record of errors on Google
  Slides or Quizlet.
• Add to this record whenever there is
  a recurrent error.
• Use as a warmer or cooler to recycle
  correction.
• Can be adapted into games like
  back-to-the-board.

Benefits:

• Helps with fossilised errors.
• Avoids the judgemental effect of
  constantly correcting the same mistake.
• Can be shared with students.

Stem correction

Method:

• Write only the stem of the incorrect
  sentence on the board.
• Students think of different ways to
  finish the sentence correctly.
• The mistake is never explicitly
  stated, but the student who made it will probably realise that it was something
  they said.

Benefits:

• Helps students upgrade language.
• Forces students to notice the
  language.
• Takes the pressure off the teacher
  and the student.

Anticipation

Method:

• Think about the errors students
  always make, especially before a certain grammar point that you have taught
  before.
• Before the activity write them up on
  the board with a big cross through them. Tell the students to be careful about
  these mistakes.

Benefits:

• Reminds students to think before
  they misspeak.
• Can be used as a visual aid if
  anyone does make the mistake.
• Makes you look like a clairvoyant.

Conclusions

Whether you are teaching 1-to-1, exam preparation or conversation classes, ensure that error correction is present in all your lessons. The expectation for correction is clear and its benefit is established.

One of the best things you can do as a teacher is aid language acquisition through targeted and effective corrective feedback that embraces the concepts of noticing and demanding high while ensuring the advancement of learners’ individual language systems.

In information theory and coding theory with applications in computer science and telecommunication, error detection and correction (EDAC) or error control are techniques that enable reliable delivery of digital data over unreliable communication channels. Many communication channels are subject to channel noise, and thus errors may be introduced during transmission from the source to a receiver. Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases.

Definitions[edit]

Error detection is the detection of errors caused by noise or other impairments during transmission from the transmitter to the receiver.

Error correction is the detection of errors and reconstruction of the original, error-free data.

History[edit]

In classical antiquity, copyists of the Hebrew Bible were paid for their work according to the number of stichs (lines of verse). As the prose books of the Bible were hardly ever written in stichs, the copyists, in order to estimate the amount of work, had to count the letters.^[1] This also helped ensure accuracy in the transmission of the text with the production of subsequent copies.^[2][3] Between the 7th and 10th centuries CE a group of Jewish scribes formalized and expanded this to create the Numerical Masorah to ensure accurate reproduction of the sacred text. It included counts of the number of words in a line, section, book and groups of books, noting the middle stich of a book, word use statistics, and commentary.^[1] Standards became such that a deviation in even a single letter in a Torah scroll was considered unacceptable.^[4] The effectiveness of their error correction method was verified by the accuracy of copying through the centuries demonstrated by discovery of the Dead Sea Scrolls in 1947–1956, dating from c.150 BCE-75 CE.^[5]

The modern development of error correction codes is credited to Richard Hamming in 1947.^[6] A description of Hamming’s code appeared in Claude Shannon’s A Mathematical Theory of Communication^[7] and was quickly generalized by Marcel J. E. Golay.^[8]

Introduction[edit]

All error-detection and correction schemes add some redundancy (i.e., some extra data) to a message, which receivers can use to check consistency of the delivered message, and to recover data that has been determined to be corrupted. Error-detection and correction schemes can be either systematic or non-systematic. In a systematic scheme, the transmitter sends the original data, and attaches a fixed number of check bits (or parity data), which are derived from the data bits by some deterministic algorithm. If only error detection is required, a receiver can simply apply the same algorithm to the received data bits and compare its output with the received check bits; if the values do not match, an error has occurred at some point during the transmission. In a system that uses a non-systematic code, the original message is transformed into an encoded message carrying the same information and that has at least as many bits as the original message.

Good error control performance requires the scheme to be selected based on the characteristics of the communication channel. Common channel models include memoryless models where errors occur randomly and with a certain probability, and dynamic models where errors occur primarily in bursts. Consequently, error-detecting and correcting codes can be generally distinguished between random-error-detecting/correcting and burst-error-detecting/correcting. Some codes can also be suitable for a mixture of random errors and burst errors.

If the channel characteristics cannot be determined, or are highly variable, an error-detection scheme may be combined with a system for retransmissions of erroneous data. This is known as automatic repeat request (ARQ), and is most notably used in the Internet. An alternate approach for error control is hybrid automatic repeat request (HARQ), which is a combination of ARQ and error-correction coding.

Types of error correction[edit]

There are three major types of error correction.^[9]

Automatic repeat request[edit]

Automatic repeat request (ARQ) is an error control method for data transmission that makes use of error-detection codes, acknowledgment and/or negative acknowledgment messages, and timeouts to achieve reliable data transmission. An acknowledgment is a message sent by the receiver to indicate that it has correctly received a data frame.

Usually, when the transmitter does not receive the acknowledgment before the timeout occurs (i.e., within a reasonable amount of time after sending the data frame), it retransmits the frame until it is either correctly received or the error persists beyond a predetermined number of retransmissions.

Three types of ARQ protocols are Stop-and-wait ARQ, Go-Back-N ARQ, and Selective Repeat ARQ.

ARQ is appropriate if the communication channel has varying or unknown capacity, such as is the case on the Internet. However, ARQ requires the availability of a back channel, results in possibly increased latency due to retransmissions, and requires the maintenance of buffers and timers for retransmissions, which in the case of network congestion can put a strain on the server and overall network capacity.^[10]

For example, ARQ is used on shortwave radio data links in the form of ARQ-E, or combined with multiplexing as ARQ-M.

Forward error correction[edit]

Forward error correction (FEC) is a process of adding redundant data such as an error-correcting code (ECC) to a message so that it can be recovered by a receiver even when a number of errors (up to the capability of the code being used) are introduced, either during the process of transmission or on storage. Since the receiver does not have to ask the sender for retransmission of the data, a backchannel is not required in forward error correction. Error-correcting codes are used in lower-layer communication such as cellular network, high-speed fiber-optic communication and Wi-Fi,^[11][12] as well as for reliable storage in media such as flash memory, hard disk and RAM.^[13]

Error-correcting codes are usually distinguished between convolutional codes and block codes:

• Convolutional codes are processed on a bit-by-bit basis. They are particularly suitable for implementation in hardware, and the Viterbi decoder allows optimal decoding.
• Block codes are processed on a block-by-block basis. Early examples of block codes are repetition codes, Hamming codes and multidimensional parity-check codes. They were followed by a number of efficient codes, Reed–Solomon codes being the most notable due to their current widespread use. Turbo codes and low-density parity-check codes (LDPC) are relatively new constructions that can provide almost optimal efficiency.

Shannon’s theorem is an important theorem in forward error correction, and describes the maximum information rate at which reliable communication is possible over a channel that has a certain error probability or signal-to-noise ratio (SNR). This strict upper limit is expressed in terms of the channel capacity. More specifically, the theorem says that there exist codes such that with increasing encoding length the probability of error on a discrete memoryless channel can be made arbitrarily small, provided that the code rate is smaller than the channel capacity. The code rate is defined as the fraction k/n of k source symbols and n encoded symbols.

The actual maximum code rate allowed depends on the error-correcting code used, and may be lower. This is because Shannon’s proof was only of existential nature, and did not show how to construct codes which are both optimal and have efficient encoding and decoding algorithms.

Hybrid schemes[edit]

Hybrid ARQ is a combination of ARQ and forward error correction. There are two basic approaches:^[10]

• Messages are always transmitted with FEC parity data (and error-detection redundancy). A receiver decodes a message using the parity information, and requests retransmission using ARQ only if the parity data was not sufficient for successful decoding (identified through a failed integrity check).
• Messages are transmitted without parity data (only with error-detection information). If a receiver detects an error, it requests FEC information from the transmitter using ARQ, and uses it to reconstruct the original message.

The latter approach is particularly attractive on an erasure channel when using a rateless erasure code.

Error detection schemes[edit]

Error detection is most commonly realized using a suitable hash function (or specifically, a checksum, cyclic redundancy check or other algorithm). A hash function adds a fixed-length tag to a message, which enables receivers to verify the delivered message by recomputing the tag and comparing it with the one provided.

There exists a vast variety of different hash function designs. However, some are of particularly widespread use because of either their simplicity or their suitability for detecting certain kinds of errors (e.g., the cyclic redundancy check’s performance in detecting burst errors).

Minimum distance coding[edit]

A random-error-correcting code based on minimum distance coding can provide a strict guarantee on the number of detectable errors, but it may not protect against a preimage attack.

Repetition codes[edit]

A repetition code is a coding scheme that repeats the bits across a channel to achieve error-free communication. Given a stream of data to be transmitted, the data are divided into blocks of bits. Each block is transmitted some predetermined number of times. For example, to send the bit pattern «1011», the four-bit block can be repeated three times, thus producing «1011 1011 1011». If this twelve-bit pattern was received as «1010 1011 1011» – where the first block is unlike the other two – an error has occurred.

A repetition code is very inefficient, and can be susceptible to problems if the error occurs in exactly the same place for each group (e.g., «1010 1010 1010» in the previous example would be detected as correct). The advantage of repetition codes is that they are extremely simple, and are in fact used in some transmissions of numbers stations.^[14][15]

Parity bit[edit]

A parity bit is a bit that is added to a group of source bits to ensure that the number of set bits (i.e., bits with value 1) in the outcome is even or odd. It is a very simple scheme that can be used to detect single or any other odd number (i.e., three, five, etc.) of errors in the output. An even number of flipped bits will make the parity bit appear correct even though the data is erroneous.

Parity bits added to each «word» sent are called transverse redundancy checks, while those added at the end of a stream of «words» are called longitudinal redundancy checks. For example, if each of a series of m-bit «words» has a parity bit added, showing whether there were an odd or even number of ones in that word, any word with a single error in it will be detected. It will not be known where in the word the error is, however. If, in addition, after each stream of n words a parity sum is sent, each bit of which shows whether there were an odd or even number of ones at that bit-position sent in the most recent group, the exact position of the error can be determined and the error corrected. This method is only guaranteed to be effective, however, if there are no more than 1 error in every group of n words. With more error correction bits, more errors can be detected and in some cases corrected.

There are also other bit-grouping techniques.

Checksum[edit]

A checksum of a message is a modular arithmetic sum of message code words of a fixed word length (e.g., byte values). The sum may be negated by means of a ones’-complement operation prior to transmission to detect unintentional all-zero messages.

Checksum schemes include parity bits, check digits, and longitudinal redundancy checks. Some checksum schemes, such as the Damm algorithm, the Luhn algorithm, and the Verhoeff algorithm, are specifically designed to detect errors commonly introduced by humans in writing down or remembering identification numbers.

Cyclic redundancy check[edit]

A cyclic redundancy check (CRC) is a non-secure hash function designed to detect accidental changes to digital data in computer networks. It is not suitable for detecting maliciously introduced errors. It is characterized by specification of a generator polynomial, which is used as the divisor in a polynomial long division over a finite field, taking the input data as the dividend. The remainder becomes the result.

A CRC has properties that make it well suited for detecting burst errors. CRCs are particularly easy to implement in hardware and are therefore commonly used in computer networks and storage devices such as hard disk drives.

The parity bit can be seen as a special-case 1-bit CRC.

Cryptographic hash function[edit]

The output of a cryptographic hash function, also known as a message digest, can provide strong assurances about data integrity, whether changes of the data are accidental (e.g., due to transmission errors) or maliciously introduced. Any modification to the data will likely be detected through a mismatching hash value. Furthermore, given some hash value, it is typically infeasible to find some input data (other than the one given) that will yield the same hash value. If an attacker can change not only the message but also the hash value, then a keyed hash or message authentication code (MAC) can be used for additional security. Without knowing the key, it is not possible for the attacker to easily or conveniently calculate the correct keyed hash value for a modified message.

Error correction code[edit]

Any error-correcting code can be used for error detection. A code with minimum Hamming distance, d, can detect up to d − 1 errors in a code word. Using minimum-distance-based error-correcting codes for error detection can be suitable if a strict limit on the minimum number of errors to be detected is desired.

Codes with minimum Hamming distance d = 2 are degenerate cases of error-correcting codes, and can be used to detect single errors. The parity bit is an example of a single-error-detecting code.

Applications[edit]

Applications that require low latency (such as telephone conversations) cannot use automatic repeat request (ARQ); they must use forward error correction (FEC). By the time an ARQ system discovers an error and re-transmits it, the re-sent data will arrive too late to be usable.

Applications where the transmitter immediately forgets the information as soon as it is sent (such as most television cameras) cannot use ARQ; they must use FEC because when an error occurs, the original data is no longer available.

Applications that use ARQ must have a return channel; applications having no return channel cannot use ARQ.

Applications that require extremely low error rates (such as digital money transfers) must use ARQ due to the possibility of uncorrectable errors with FEC.

Reliability and inspection engineering also make use of the theory of error-correcting codes.^[16]

Internet[edit]

In a typical TCP/IP stack, error control is performed at multiple levels:

• Each Ethernet frame uses CRC-32 error detection. Frames with detected errors are discarded by the receiver hardware.
• The IPv4 header contains a checksum protecting the contents of the header. Packets with incorrect checksums are dropped within the network or at the receiver.
• The checksum was omitted from the IPv6 header in order to minimize processing costs in network routing and because current link layer technology is assumed to provide sufficient error detection (see also RFC 3819).
• UDP has an optional checksum covering the payload and addressing information in the UDP and IP headers. Packets with incorrect checksums are discarded by the network stack. The checksum is optional under IPv4, and required under IPv6. When omitted, it is assumed the data-link layer provides the desired level of error protection.
• TCP provides a checksum for protecting the payload and addressing information in the TCP and IP headers. Packets with incorrect checksums are discarded by the network stack, and eventually get retransmitted using ARQ, either explicitly (such as through three-way handshake) or implicitly due to a timeout.

Deep-space telecommunications[edit]

The development of error-correction codes was tightly coupled with the history of deep-space missions due to the extreme dilution of signal power over interplanetary distances, and the limited power availability aboard space probes. Whereas early missions sent their data uncoded, starting in 1968, digital error correction was implemented in the form of (sub-optimally decoded) convolutional codes and Reed–Muller codes.^[17] The Reed–Muller code was well suited to the noise the spacecraft was subject to (approximately matching a bell curve), and was implemented for the Mariner spacecraft and used on missions between 1969 and 1977.

The Voyager 1 and Voyager 2 missions, which started in 1977, were designed to deliver color imaging and scientific information from Jupiter and Saturn.^[18] This resulted in increased coding requirements, and thus, the spacecraft were supported by (optimally Viterbi-decoded) convolutional codes that could be concatenated with an outer Golay (24,12,8) code. The Voyager 2 craft additionally supported an implementation of a Reed–Solomon code. The concatenated Reed–Solomon–Viterbi (RSV) code allowed for very powerful error correction, and enabled the spacecraft’s extended journey to Uranus and Neptune. After ECC system upgrades in 1989, both crafts used V2 RSV coding.

The Consultative Committee for Space Data Systems currently recommends usage of error correction codes with performance similar to the Voyager 2 RSV code as a minimum. Concatenated codes are increasingly falling out of favor with space missions, and are replaced by more powerful codes such as Turbo codes or LDPC codes.

The different kinds of deep space and orbital missions that are conducted suggest that trying to find a one-size-fits-all error correction system will be an ongoing problem. For missions close to Earth, the nature of the noise in the communication channel is different from that which a spacecraft on an interplanetary mission experiences. Additionally, as a spacecraft increases its distance from Earth, the problem of correcting for noise becomes more difficult.

Satellite broadcasting[edit]

The demand for satellite transponder bandwidth continues to grow, fueled by the desire to deliver television (including new channels and high-definition television) and IP data. Transponder availability and bandwidth constraints have limited this growth. Transponder capacity is determined by the selected modulation scheme and the proportion of capacity consumed by FEC.

Data storage[edit]

Error detection and correction codes are often used to improve the reliability of data storage media.^[19] A parity track capable of detecting single-bit errors was present on the first magnetic tape data storage in 1951. The optimal rectangular code used in group coded recording tapes not only detects but also corrects single-bit errors. Some file formats, particularly archive formats, include a checksum (most often CRC32) to detect corruption and truncation and can employ redundancy or parity files to recover portions of corrupted data. Reed-Solomon codes are used in compact discs to correct errors caused by scratches.

Modern hard drives use Reed–Solomon codes to detect and correct minor errors in sector reads, and to recover corrupted data from failing sectors and store that data in the spare sectors.^[20] RAID systems use a variety of error correction techniques to recover data when a hard drive completely fails. Filesystems such as ZFS or Btrfs, as well as some RAID implementations, support data scrubbing and resilvering, which allows bad blocks to be detected and (hopefully) recovered before they are used.^[21] The recovered data may be re-written to exactly the same physical location, to spare blocks elsewhere on the same piece of hardware, or the data may be rewritten onto replacement hardware.

Error-correcting memory[edit]

Dynamic random-access memory (DRAM) may provide stronger protection against soft errors by relying on error-correcting codes. Such error-correcting memory, known as ECC or EDAC-protected memory, is particularly desirable for mission-critical applications, such as scientific computing, financial, medical, etc. as well as extraterrestrial applications due to the increased radiation in space.

Error-correcting memory controllers traditionally use Hamming codes, although some use triple modular redundancy. Interleaving allows distributing the effect of a single cosmic ray potentially upsetting multiple physically neighboring bits across multiple words by associating neighboring bits to different words. As long as a single-event upset (SEU) does not exceed the error threshold (e.g., a single error) in any particular word between accesses, it can be corrected (e.g., by a single-bit error-correcting code), and the illusion of an error-free memory system may be maintained.^[22]

In addition to hardware providing features required for ECC memory to operate, operating systems usually contain related reporting facilities that are used to provide notifications when soft errors are transparently recovered. One example is the Linux kernel’s EDAC subsystem (previously known as Bluesmoke), which collects the data from error-checking-enabled components inside a computer system; besides collecting and reporting back the events related to ECC memory, it also supports other checksumming errors, including those detected on the PCI bus.^[23][24][25] A few systems^[specify] also support memory scrubbing to catch and correct errors early before they become unrecoverable.

See also[edit]

• Berger code
• Burst error-correcting code
• ECC memory, a type of computer data storage
• Link adaptation
• List of algorithms § Error detection and correction
• List of hash functions

References[edit]

Further reading[edit]

• Shu Lin; Daniel J. Costello, Jr. (1983). Error Control Coding: Fundamentals and Applications. Prentice Hall. ISBN 0-13-283796-X.
• SoftECC: A System for Software Memory Integrity Checking
• A Tunable, Software-based DRAM Error Detection and Correction Library for HPC
• Detection and Correction of Silent Data Corruption for Large-Scale High-Performance Computing

External links[edit]

• The on-line textbook: Information Theory, Inference, and Learning Algorithms, by David J.C. MacKay, contains chapters on elementary error-correcting codes; on the theoretical limits of error-correction; and on the latest state-of-the-art error-correcting codes, including low-density parity-check codes, turbo codes, and fountain codes.
• ECC Page — implementations of popular ECC encoding and decoding routines

Unlike ESL students, who take advantage of living in countries that English is widely used on a regular basis, people who try to learn English as a foreign language or EFL learners’ exposure to English is inevitably limited to those three to four hours a week that they spend in academic environments. Their needs are consequently a little bit different from ESL students.

Regarding the limited sources, they have access to, including teachers’ talk and textbook audios that are unnaturally slow and way too clear, EFL students, therefore, need to look for more authentic and genuine materials in order to provide themselves with a better quality of input and improve their listening and speaking skills. Some recommended sources like YouTube videos, English movies, series, and so forth consistently help them enhance their receptive skills, but when it comes to productive skills, specifically speaking, these students might have been able to improve their fluency using the suggested sources, but the importance of accuracy appears to be neglected.

So what can an EFL teacher do in order to improve the accuracy and fluency of their students?

Constructive error treatment, which is a familiar aspect of teaching for all the teachers around the world, needs to be more valued in a situation like this since it is a very crucial skill for a teacher to know when and how students’ errors should be dealt with before it is too late.

Self-correction

This is a chance you give your students to look back, analyze and think about what they have just said in order to correct their own errors and avoid repeating the same mistake again by attracting their full attention to the corrected form.

There are lots of techniques applied by teachers in order to promote self-correction in their classes, including a variety of appropriate gestures and facial expressions. To notify students of their mistakes, you can also code your gestures like pointing back and front for past and future tenses or shaping an imaginary mustache for propitious male and female pronouns usage.

Don’t forget that too much correction like this gradually makes students dependent on their constant eye contact with you and disturbs student-to-student eye contact, which is a necessary feature for a more student-centered class.

Some teachers use a colored flag and shake it to spot a mistake when students are talking. A Mr.Noman puppet also does the same thing by reacting to students’ mistakes.

If you want your students to repeat what they said in a corrected form, cup your ear with your palm, show a puzzled facial expression, or simply ask them to repeat what they said by using proper phrases.

Another thing you can do is repeating their sentences and pausing before a specific mistake.

• Student: «He opened the door and took her keys.»
• Teacher: «He opened the door and took…?»
• Student: «He opened the door and took his keys.»

If it is still hard for the student to spot the error, you can try giving options:

• Student: «He opened the door and took her keys.»
• Teacher: «He opened the door and took her or his keys?»
• Student: «He opened the door and took his keys.»

Writing assignments also give students the think-time they need to correct their own mistakes. You can highlight their mistakes and start teaching them writing correction codes like SP for spelling mistakes or WT for the wrong tense from very early levels. When they know the whereabouts and type of the error, they can correct it easily.

If an error is recurring or a specific student keeps repeating the same mistake, it is probably fossilized. Write it on a piece of paper and assign the student to correct it. Keep doing this every time you hear the same error until it disappears.

Notice that native speakers of English or any other languages don’t normally tend to correct their own mistakes, so self-correction is not considered a natural habit and leads to poorer results in exams like IELTS.

Peer-correction

If a student is not able to recognize and correct his/her mistakes, you might want to give other students the chance to correct their counterparts’ errors. It helps them with their listening skills and makes them focus and listen cautiously and aimfully. You can also reduce your talking time and increase students’ talking time and participation. It is not a very popular approach, though, since it sometimes gets very noisy when the whole class tries to correct somebody’s mistake.

In order to avoid jumping on a trembling student like a wolf pack to correct his/her mistake, ask students to make notes while they are listening and correct them later.

You can also exchange writing assignments and ask students to correct their classmates’ mistakes.

Teacher-correction

This is the most popular type of correction among both students and teachers and probably the last thing you are supposed to do as a teacher. Give students the chance to correct themselves as much as possible, get help from their classmates, and if they really can’t handle it, you are the last person who can intervene and help them correct the error.

If your task is not aimed for accuracy, in order to avoid interrupting the flow of speech, make notes while the activity is in process and you are monitoring. After the feedback on the task is aimfully provided, feedback on language can be applied by boarding the errors you made notes of, and students can correct them in pairs or groups. If you start boarding the errors before the task is done, you probably attract too much unwanted attention and cause distraction from the task, so just let them focus on the task and do it later.

There is a preference to correct pronunciation errors on the spot, but if you have made notes of some, choral and individual drilling help students recall and learn the correct pronunciation.

Are you ready to teach English abroad or online?

Eventually, the country and the culture you are teaching in and the age of students can affect the quality of your feedback on language. Although younger learners are more receptive and less embarrassed when corrected, it’s logical to conclude that overcorrection is demotivating, kills creativity, and makes students feel insecure and unsure about their abilities.

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HOT or COLD?

As English teachers, we know that making mistakes is the proof of learning, but the question is how we can handle these mistakes. We need to sharpen our error correction skills in order not to demotivate our students.

There are two kinds of error correction techniques:

1. Hot correction: As soon as we notice a student making an error while we are presenting the language or practicing activities, we can ask CCQs (concept checking questions) that focus on meaning and form.We should encourage self correction first and then peer correction if needed.

Also within hot correction, we can use Quick fire Drills, these are:

• Repetition drills: In this type,teacher first models the target language then students at first drill chorally, then individually.
• Backchaining: For longer utterences this is a useful type. In it the language is in chunks and it is drilled from the end backwards.

e.g. If I see him, I’ll tell him.

t: tell him

Ss: tell him

t: I’ll tell him

  Ss: I’ll tell him

t: see him I’ll tell him

 Ss: see him I’ll tell him

t: If I see him I’ll tell him

Ss: If I see him I’ll tell him

• Transformation drills: to manipulate a grammatical structure, this type is a good one.

t: I’ve got some apples. Negative?

S1: I haven’t got any apples.

t: He has got some peers. Negative?

S2: He hasn’t got any pears.

• Chain drill: This type focuses more on sts. and it’s a bit more complicated.

S1: I like swimming.

t: So do I.

S2: I like riding a bike.

t: So do I.

Students then do the drill:

S1: I like swimming.

S2: So do I. I like reading.

S3: So do I. I like playing golf. etc.

2.  Cold correction: In order not to interrupt the learner during a speaking activity- as we are focusing more on oral fluency- , we need to monitor and record the language of the learner to focus on the errors when the activity is complete.

Besides speaking activities, we can use cold correction with writing activities as well. We can have them write a text in class or at home and after checking the texts, we can choose one sentence from each student’s text that has an error in it. After that we can use these sentences in the class to give whole class feedback without addressing the students.