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Low-density parity-check codes. (Коды с малой плотностью проверок на четность. Translation from the English by A. Sheverdyaev. Edited by R. L. Dobrushin.) (English. Russian translation) Zbl 0156.40701
Cambridge, MA: MIT Press. 90 p. (1963); Biblioteka Sbornika “Matematika”. Moskva: Izdat. ’Mir’ 144 p. (1966).
This monograph presents a technique for achieving high data rates and negligible error probabilities on noisy channels with a reasonable amount of equipment. The chapters of the monograph are arranged in such a way that with the exception of chapter 5 each chapter can be read independently of the others.
Chapter 1 sets the background of the study, summarizes the results, and briefly compares low-density coding with other coding schemes. Chapter 2 analyzes the distance between code words in low-density codes and Chapter 3 applies these results to the problem of bounding the probability of decoding error that can be achieved for these codes on a broad class of binary input channels. The results of Chapter 3 can be immediately applied to any code or class of codes for which the distance properties can be bounded. Chapter 4 presents a simple decoding algorithm for these codes and analyzes the resulting error probability. Chapter 5 briefly extends all the previous results to multi-input channels, and Chapter 6 presents the results of computer simulation of the low-density decoding algorithm.

94-02 Research exposition (monographs, survey articles) pertaining to information and communication theory
94B05 Linear codes, general
94B35 Decoding
94B70 Error probability in coding theory
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