A practical reliability metric for block codes used on binary-input channels

A reliability metric (RM) for a block code is defined to be a function that operates on both the decoder input (a block of channel output) and the decoder output (the codeword estimate) and produces a real number as a measure of the reliability of the decoder decision. The best RM has the disadvantage of depending on the codeword probabilities. Thus, the ideal RM is defined as the value that would be computed for equally likely codewords. The implementation of the ideal RM is too costly for most applications. The author proposes an easily implemented RM for binary-input memoryless channels (for state-observable channels with a freely evolving state such as some fading channels) when the codewords consist of n 2^m-ary symbols, each of which is transmitted serially by m uses of the channel. Simulation results for some BCH codes and some Reed-Solomon codes used in a simple ARQ system show that the proposed RM performs nearly as well as the ideal RM and much better than a previously proposed practical RM