Abstract
This is a complete presentation of all important theoretical and experimental work done on low-density codes. Low-density coding is one of the three techniques thus far developed for efficient communication over noisy channels with an arbitrarily low probability of error. A principal result of information theory is that if properly coded information is transmitted over a noisy channel at a rate below channel capacity, the probability of error can be made to approach zero exponentially with the code length. Any practical use of this theorem, however, requires a coding scheme in which the cost of storage and computation equipment grows slowly with code length. The present book analyzes a class of coding schemes for which costs grow approximately linearly with code length. It demonstrates that error probability approaches zero exponentially with a root of the block length and cites experimental evidence that this coding scheme has profitable aplicability in many communications situations.
Keywords
Low-density parity-check codeCoding (social sciences)Variable-length codeAlgorithmProbability of errorCode rateComputer scienceTheoretical computer scienceMathematicsCoding gainUniversal codeChannel codeExponential growthStatisticsDecoding methodsSystematic code
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Publication Info
- Year
- 1963
- Type
- book
- Citations
- 4319
- Access
- Closed
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Cite This
Robert G. Gallager
(1963).
Low-Density Parity-Check Codes.
The MIT Press eBooks
.
https://doi.org/10.7551/mitpress/4347.001.0001
Identifiers
- DOI
- 10.7551/mitpress/4347.001.0001