A lower bound on the mismatched Viterbi decoding bit-error-rate

Abstract

A lower bound is derived on the bit-error-rate that results when a rate 1/n convolutionally encoded binary data stream is transmitted over a noisy symmetric channel, and is then decoded using a mismatched Viterbi decoder, i.e., a Viterbi decoder that performs maximum-likelihood sequence estimation using possibly incorrect branch metrics. The branch metrics are assumed to be symmetric, but are generally different from the log-likelihood function. The lower bound is applied to the study of convolutionally encoded direct-sequence spread-spectrum communication with Laplacian noise, and it is shown that nearest-neighbor decoding, which is optimal for Gaussian noise, is sub-optimal and asymptotically (for high processing gain) results in a 3 dB loss in performance when compared with the optimal maximum-likelihood decoder.