RECORD
Channels with Synchronization/Substitution Errors and Computation of Error Control Codes
Information Theory · Submitted 23 Jan 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim If the algorithm finds less than $N$ codewords, then those codewords constitute a code that is \ff-maximal with high probability.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We introduce the concept of an \ff-maximal error-detecting block code, for some parameter \ff{} between 0 and 1, in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. Our motivation for this is that constructing a maximal error-detecting code is a computationally hard problem. We present a randomized algorithm that takes as input two positive integers $N,\ell$, a probability value \ff, and a specification of the errors permitted in some application, and generates an error-detecting, or error-correcting, block code having up to $N$ codewords of length $\ell$. If the algorithm finds less than $N$ codewords, then those codewords constitute a code that is \ff-maximal with high probability. The error specification (also called channel) is modelled as a transducer, which allows one to model any rational combination of substitution and synchronization errors. We also present some elements of our implementation of various error-detecting properties and their associated methods. Then, we show several tests of the implemented randomized algorithm on various channels. A methodological contribution is the presentation of how various desirable error combinations can be expressed formally and processed algorithmically.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We introduce the concept of an \ff-maximal error-detecting block code, for some parameter \ff{} between 0 and 1, in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. | contribution 1.00 | 0.91 | 0.08 | asserted 0.99 |
| s1 | Our motivation for this is that constructing a maximal error-detecting code is a computationally hard problem. | background 0.91 | 0.12 | 0.04 | asserted 1.00 |
| s2 | We present a randomized algorithm that takes as input two positive integers $N,\ell$, a probability value \ff, and a specification of the errors permitted in some application, and generates an error-detecting, or error-correcting, block code having up to $N$ codewords of length $\ell$. | method 0.69 | 0.94 | 0.14 | asserted 0.98 |
| s3 | If the algorithm finds less than $N$ codewords, then those codewords constitute a code that is \ff-maximal with high probability. | result 0.61 | 0.87 | 0.20 | asserted 0.56 |
| s4 | The error specification (also called channel) is modelled as a transducer, which allows one to model any rational combination of substitution and synchronization errors. | method 0.98 | 0.63 | 0.04 | asserted 0.99 |
| s5 | We also present some elements of our implementation of various error-detecting properties and their associated methods. | contribution 0.53 | 0.91 | 0.03 | asserted 0.97 |
| s6 | Then, we show several tests of the implemented randomized algorithm on various channels. | contribution 0.46 | 0.95 | 0.07 | asserted 1.00 |
| s7 | A methodological contribution is the presentation of how various desirable error combinations can be expressed formally and processed algorithmically. | contribution 0.98 | 0.91 | 0.12 | asserted 0.99 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We introduce the concept of an \ff-maximal error-detecting block code, for some parameter \ff{} between 0 and 1, in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. Our motivation for this is that constructing a maximal error-detecting code is a computationally hard problem. We present a randomized algorithm that takes as input two positive integers $N,\ell$, a probability value \ff, and a specification of the errors permitted in some application, and generates an error-detecting, or error-correcting, block code having up to $N$ codewords of length $\ell$. If the algorithm finds less than $N$ codewords, then those codewords constitute a code that is \ff-maximal with high probability. The error specification (also called channel) is modelled as a transducer, which allows one to model any rational combination of substitution and synchronization errors. We also present some elements of our implementation of various error-detecting properties and their associated methods. Then, we show several tests of the implemented randomized algorithm on various channels. A methodological contribution is the presentation of how various desirable error combinations can be expressed formally and processed algorithmically.
Human review
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 1 sentence without a confident label
Uses the method or tool of 1 paper
-
All main algorithmic tools have been implemented over the years in the Python package FAdo [ref] .
Symbolic Manipulation of Code Properties · Implementation and Use · 0.98
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.