A Comparison of Rateless Codes at Short Block Lengths

Raptor codes and rate-compatible low-density parity-check (RC-LDPC) codes have drawn much attention in recent years as they can approach channel capacity without requiring channel information at the transmitter. Raptor codes have been shown to uniformly approach the binary-input AWGN channel capacity, especially at low SNR´s, whereas RC-LDPC codes have the potential to provide higher throughput than Raptor codes at high SNR´s. In this paper, we use different message word sizes to compare the throughput of three rateless codes, namely, Raptor codes, rate-compatible irregular repeat-accumulate (RC-IRA) codes, and the rate-compatible quasi-cyclic LDPC (RC/QC-LDPC) codes proposed in the 3GPP2 and 802.20 standards. The comparison is focused on short message word lengths under 16-symbol quadrature amplitude modulation (16-QAM). The simulation results in the AWGN channel show that RC-IRA and RC/QC-LDPC codes outperform Raptor codes at high SNR´s. Under frequency flat Rayleigh fading channels, RC-IRA codes outperform RC/QC-LDPC codes at high SNR´s and perform slightly worse at low SNR´s. We also show that for short block lengths, the throughput of RC-IRA codes is not particularly sensitive to the mother code rate, the belief propagation (BP) algorithm scheduling, the existence of parallel edges during check node combining, and the symbol degree distribution (for fixed average left degree).