Performance of short polar codes under ML decoding (original) (raw)

Polar codes are a recently introduced class of codes that achieve the capacity of arbitrary symmetric binary-input channels. This capacity-achieving performance is obtained by encoders and decoders of complexity O(N log N) where N is the code block-length. The performance of polar coding under belief propahation (BP) decoding has been studied before, using Reed-Muller (RM) codes as a benchmark. This work studies the performance of polar coding under trellis-based maximum-likelihood (ML) decoding, again using RM codes as a benchmark. One finding is that RM codes perform better than polar codes under ML decoding for certain short codes. On the other hand, polar codes have a lower trellis complexity. A second finding is that BP decoding offers performance comparable to ML decoding as the block-length is increased.