Abstract
Soft decision decoding of binary linear block codes transmitted over the additive white Gaussian channel (AWGN) using antipodal signaling is considered. A set of decoding algorithms called generalized Chase algorithms is proposed. In contrast to Chase algorithms, which require a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lfloor (d- 1)/2 \rfloor</tex> binary error-correcting decoder for decoding a binary linear block code of minimum distance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</tex> , the generalized Chase algorithms can use a binary decoder that can correct less than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lfloor ( d - 1)/2 \rfloor</tex> hard errors. The Chase algorithms are particular cases of the generalized Chase algorithms. The performance of all proposed algorithms is asymptotically optimum for high signal-to-noise ratio (SNR). Simulation results for the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(47, 23)</tex> quadratic residue code indicate that even for low SNR the performance level of a maximum likelihood decoder can be approached by a relatively simple decoding procedure.
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