Coding performance of hybrid ARQ schemes

We develop a unified performance metric and detailed analysis for hybrid automatic repeat request (HARQ) schemes based on incremental redundancy (IR) and Chase combining (CC). The general result is applicable to both symbol-based and bit-interleaved coded modulations, to HARQ processes based on rateless and fixed-rate mother codes, and IR schemes with and without a self-decodability restriction. The analysis shows that IR over CC coding gains tend to increase with the initial coding rate, but decrease with the signal-to-noise (SNR) variation between retransmissions. The gains can also be diminished when a fixed-rate mother code is used or when the self-decodability criterion is imposed. The theoretical prediction is compared with observed gains at 10% codeword error rates based on turbo-coding simulations. For scenarios with moderately varying SNR between retransmissions, the analytical model tracks actual simulation results very well. However, when the SNR varies widely and the systematic part of the turbo codeword is effectively erased, the CC scheme could, in fact, outperform some IR schemes. For these scenarios, which can be induced by fast time-varying fading or long retransmission delays, the self-decodable IR and the CC schemes prove to be more robust without much performance comprise. Finally, we discuss adaptive improvement to the conventional IR schemes based on the analytical result.