On Performance and Complexity of OSD for Short Error Correcting Codes in 5G-NR

We compare the performance of a selection of short and very short length linear binary codes on the binary-input Gaussian channel. We use the probabilistic Ordered Statistics Decoder, that is universal to any code construction. As such we compare codes and not decoders. The word error rate versus the channel parameter is found for LDPC, Reed-Muller, Polar, Turbo, Golay and BCH codes at length 20, 32 and 256 bits. BCH and random codes outperform other codes in absence of a cyclic redundancy check. Under joint decoding, the concatenation of a cyclic redundancy check makes all codes perform very close to optimal lower bounds. Optimizations of the Ordered Statistics Decoder are discussed and revealed to bring near-ML performance with a notable complexity reduction for very short length codes at an affordable complexity.