Gallager error-correcting codes for binary asymmetric channels

Gallager error-correcting codes for binary asymmetric channels

Abstract. We derive critical noise levels for Gallager codes on asymmetric channels as a function of the input bias and the temperature. Using a statistical mechanics approach we study the space of codewords and the entropy in the various decoding regimes. We further discuss the relation of the convergence of the message passing algorithm with the endogenous property and complexity, characteriz...

Asymmetric quantum error correcting codes

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Regular and Irregular Gallager - type Error - Correcting Codes

The performance of regular and irregular Gallager-type errorcorrecting code is investigated via methods of statistical physics. The transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse matrices; the number of non-zero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity may be sat...

Regular and Irregular Gallager-zype Error-Correcting Codes

Error Correcting Codes for Satellite Communication Channels

This paper addresses the problem of efficient forward error correction on differentially encoded, quadriphase-shift-keying (DQPSK) channels. The approach is to design codes to correct the most probable error patterns. First the probability distribution of error patterns is derived. Then a class of convolutional codes that correct any single two-bit error is described. Finally a threshold decoda...