Error exponents for block Markov superposition encoding with varying decoding latency

Abstract

Block Markov superposition encoding has been used on a number of channels to enable transmitter cooperation, including the decode-and-forward (DF) relaying scheme on the full-duplex relay channel. We analyze the error performance of DF with regular encoding and sliding window decoding as the window size of the decoder is allowed to grow. Specifically, we use Gallager's random coding exponent to analyze the behavior of DF in the finite block length regime where the error probability cannot be made arbitrarily small for a fixed rate and block length. Although using a larger decoding window may not result in a better achievable rate in the infinite block length regime, doing so for finite block lengths enables a higher rate of transmission for a given error probability. In particular, these rate enhancements can lead to a larger range of operating scenarios in which relaying can outperform direct transmission.