On two probabilistic decoding algorithms for binary linear codes

A generalization of Sullivan inequality on the ratio of the probability of a linear code to that of any of its cosets is proved. Starting from this inequality, a sufficient condition for successful decoding of linear codes by a probabilistic method is derived. A probabilistic decoding algorithm for “low–density parity–check codes” is also analyzed. The results obtained allow one to estimate experimentally the probability of successful decoding using these probabilistic algorithms. Index Terms — linear code, inequality, probabilistic decoding, low– density parity–check code ∗The author is with the Institute of Applied Mathematics and Electronics, Belgrade, Yugoslavia