Block Error Probability using List Viterbi Decoding with Hard Decisions

We consider the List Viterbi Algorithm (LVA) for block decoding of a concatenated channel coding system. The inner code is either convolutional or rate compatible punctured convo-lutional (RCPC), and the outer code is a cyclic redundancy check (CRC). The block error probability is deened as the probability that the transmitted sequence is not in the list of L candidates considered by the LVA. We derive approximations for the block error probability for both the additive white Gaussian noise (AWGN) and frequency non-selective Rayleigh fading channels with hard decisions. We show that the approximations approach simulation results as the signal-to-noise ratio becomes large. From our results, we see that a list length of L = 2 can ooer a one decade improvement in block error probability over L = 1 for both channels. The asymptotic gain in signal-to-noise ratio for L = 2 over L = 1 is shown to be about 0.7-0.9 dB over an AWGN channel, and about 3-5 dB over a Rayleigh fading channel.