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IEEE Transactions on Information Theory

Majority decoding the nonorthogonal parity checks (Corresp.)

Chin-Long Chen

Published Nov 1, 1976• 1 citation
Publisher

Abstract

A new bound on the error-correcting capability of majority decoding using nonorthogonal parity checks is derived. The new bound is then applied to a class of Euclidean geometry codes.
DOI
10.1109/tit.1976.1055632

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Hard decision decoding of low density parity check (LDPC) codes has potential applications in practical settings like data storage. For this purpose, it is important for the code to have an assured minimum distance and, hence, guaranteed error correction capability. In this paper, we show that with very high probability the guaranteed error correction capability of Euclidean geometry (EG) codes using threshold-optimized, iterative majority logic (ML) decoding is much greater than the usual single iteration ML decoding, making these codes much more attractive for hard decision decoding. For instance, the (262143, 242461, t/spl ges/256) EG code (a (512, 512)-regular LDPC code) can correct t=580 bit errors with probability better than 1-1/spl times/10/sup -58/.