Class of algorithms for decoding block codes with channel measurement information

Abstract

A class of decoding algorithms that utilizes channel measurement information, in addition to the conventional use of the algebraic properties of the code, is presented. The maximum number of errors that can, with high probability, be corrected is equal to one less than d, the minimum Hamming distance of the code. This twofold increase over the error-correcting capability of a conventional binary decoder is achieved by using channel measurement (soft-decision) information to provide a measure of the relative reliability of each of the received binary digits. An upper bound on these decoding algorithms is derived, which is proportional to the probability of an error for dth order diversity, an expression that has been evaluated for a wide range of communication channels and modulation techhiques. With the aid of a lower hound on these algorithms, which is also a lower hound on a correlation (maximumlikelihood) decoder, we show for both the Gaussian and Rayleigh fading channels, that as the signal-to-noise ratio (SNR) increases, the asyniptotic behavior of these decoding algorithms cannot be improved. Computer simulations indicate that even for low SNR the performance of a correlation decoder can be approached by relatively simple decoding procedures. In addition, we study the effect on the performance of these decoding algorithms when a threshold is used to simplify the decoding process.

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