Writing Correction Code Pdf

[Kerby Kolpack]

Youshow the learners where the mistakes are and what kind they are, and then they try to correct them as a second stage to the initial writing task. The codes shown here are just an example and are not meant to all be used at every level. You need to find out which ones work for you and your learners.

Which quantum error correction code currently holds the record in terms of the highest threshold for fault-tolerance? I know that the surface code is pretty good ($\approx10^-2$?), but finding exact numbers is difficult. I also read about some generalizations of the surface code to 3D clusters (topological quantum error correction). I guess the main motivation for this research was to increase the threshold for calculations of arbitrary length.

In order to judge this value it would be nice to know what threshold is theoretically achievable. So if you know of (non-trivial) upper bounds on thresholds for arbitrary quantum error correction codes that would be nice.

Exact threshold numbers mean you need a specific error model, as you know. And for that you need a decoder, which ideally adapts to the specifics of the error model while remaining fast enough to keep up. Your definition of what is fast enough for the task at hand will have a big effect on what the threshold is.

To get upper bounds for a specific code and specific noise model, we can sometimes map the model to one of statistical mechanics. The threshold then corresponds to the point of a phase transition. See this paper for an example of how to do this, and the references therein for others.

Other than the threshold, another important factor is how easy it is to do quantum computation on the stored information. The surface code is quite bad at this, which is a major reason that people still consider other codes, despite the great advantages of the surface codes.

I believe that the Centre for Engineered Quantum Systems, School of Physics, The University of Sydney and the Center for Theoretical Physics, Massachusetts Institute of Technology use of a tensor network decoder of Bravyi, Suchara and Vargo (BSV), to achieve the highest error correction threshold to date.

The idea was roughly to make use of a well-known connection between error correction codes and distillation of multiple noisy Bell states into a single, less noisy Bell state. In essence, if you have multiple noisy Bell states, one strategy for making a single high quality Bell state is to teleport the codewords of an error correction code through them. It's a two-way relationship; if you come up with a better distillation strategy, that defines a better error correcting code and vice-versa. So, I wondered what would happen if you allowed a concatenated scheme of distillation of noisy Bell pairs, but allowed some errors to occur when applying the various operations. This would map directly to fault tolerance via concatenated error correcting codes. But the different perspective allowed me to estimate a threshold beyond which the noise accumulation would simply be too high, and thus the error correction scheme would fail.

Different works have made different assumptions. For example, this one restricts to specific gate sets, and derives an upper bound to the fault-tolerant threshold of 15% in a specific case (but then the question arises as to why you wouldn't pick the scheme with the highest upper bound, rather than the lowest!).

This document provides a code for correcting writing errors with abbreviations for each type of error. The code includes abbreviations for errors involving plural/singular forms, wrong words, word order, tense, word form, subject verb agreement, missing words, links, spelling, deleting words, punctuation, developing ideas, clause structure, and sentence structure.Read less

I have learned from my experiences teaching English composition that if I simply correct student errors, they are quite likely to make the same mistakes again and again. Instead, using Google Docs, I highlight a portion of their text and comment with a code that indicates the type of correction needed. Below are the codes that I use, along with explanations and examples.

The second answer might be Reed-Solomon error correcting codes (for example, using rsbep). However, this is also a problem, because from my understanding, Reed-Solomon codes don't correct insertion/deletion errors, which are probably more likely than substitution errors in this case.

If you want people to be able to read and write the data, the problem with Base64 and many text encodings is that they use characters like I, l, 1, , /, 0, O, o, and so on that people confuse with each other.

Let's say you have Red, Green, Blue and Black. You can write a script that turns your data into a collection of letters from RGBY, eg: RGBYGBRYBGBYRYYBYBRYYG (or even Red Green Blue Black Green Blue Red Black... in an Excel sheet) and back again. It's just a matter of base converting your binary data from base 2 (or hexadecimal data from base 16) to the base in the amount of colors you take (4 in this example).

Now, the most logical approach would be to get yourself 16 colors. This way, you have to use 4 times less dots which makes switching between the pens worth it. This allows you to write 4 times as much data on the paper if you need to, or perhaps have can be 4 times less accurate when putting your dots, the scaling is up to you. I would really advise against drawing every single bit.

This makes it even useful to use something like Base 32 (or Base 36). Note that the Q and 9 are the same, so you will want the top right pixel of the Q to be White for a clear distinction. Base 32 only requires a 53 x 53 grid for your example, plus a small bit of spacing to distinct between letters.

I'd recommend, along the lines of Oliver's suggestion, that you increase your data density by borrowing a page from Bacon's cipher, which prison gangs often use to encode hidden messages in missives written in 2 different script styles--usually either upper vs. lowercase characters or print vs. cursive characters, e.g.

However, since your goal isn't stegnography, you would simply use this to expand your glyph set. Doing this, you could have up to 114 glyphs just using print & cursive alphanumeric characters, or 12996 code points using dual-character encoding.

However, since all glyph counts greater than 15 and less than 256 are essentially the same for a straight cipher of binary data (meaning, you'll still need 2 characters to represent each byte, giving you a data density of 4 bits per character in all cases), you can use the extra 98 glyphs / 12740 code points for error detection/correction.

You can use this to represent 2500+ of the 4096 possible 1.5 byte values. Similarly, you could use just 16 sets to represent all values of the following byte, giving you 100% redundancy without increasing your encoded data length.

To further reduce copying errors, I would display the encoded content in gridlines and copy onto graphing paper. If you can use custom stationary that has alternating column/row colors or a chessboard-style checkered grid with lettered columns & numbered rows for quick look-ups, that would further increase copying accuracy.

You can also combine an alternating grid layout with alternating character styles as an easy form of error detection. I.e. if odd columns are always capitalized, if the transcriber finds themselves writing lowercase letters in odd columns, then they know they've made an error and can start tracking back to see where it happened.Though if your main priority is accuracy, I would use a binary encoding + Hamming code. Using a (12, 8) shortened Hamming code on standard graphing paper, you might only fit 187 bytes, encoding only 124 bytes of data. But it could be transcribed very quickly (a slash for 1, nothing for 0) and provide single error correction. Tacking on an extra parity bit (13, 8) would provide SECDED (single error correction, double error detection). Using a standard hamming code like (15, 11) or (31, 26), you get even better efficiency with 137 and 156 bytes of data per sheet, respectively. Even higher code rates can be achieved, depending on how accurate you think your transcriber can be.

We used to use S-Records for this purpose. There was a simple checksum, per line, for error detection. Normally all but the last line was fixed length, so the end-of-line marker served as a check for insertions and deletions. There was no check for missing lines though. For this we simply counted the number of lines. Mostly files were short, less than 100 lines, but I do remember at least one which had 300 lines or more. It was very tedious typing files into the system. Of course, among the first programs transferred this way was a downloader ;)

Schools have long used OMR for testing; the forms are simple to use and to read, and accuracy is typically better than keyboard input. For higher accuracy, commercial manufacturers like Scantron and ReMark can create custom forms.

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