Efficient approximate ML decoding units for polar list decoders

Polar codes are of great interest since they are the first provably capacity-achieving forward error correction codes. To improve throughput of polar decoders, maximum likelihood (ML) decoding units are used by successive cancellation list (SCL) decoders as well as successive cancellation (SC) decoders. In this paper, an approximate ML (AML) decoding unit with reduced complexity for SCL decoders is proposed. In particular, we investigate the distribution of frozen bits of polar codes designed for the binary erasure channel and additive white Gaussian noise channel, and take advantage of the distribution to reduce the complexity of the AML decoding unit. Simulation and synthesis results show that the proposed AML decoding unit has much lower complexity.