Fast List Decoders for Polar Codes

TL;DR

This paper introduces a new unrolled list decoding algorithm for polar codes that significantly increases decoding speed, making it competitive with or faster than LDPC decoders in software-defined radio applications.

Contribution

The paper presents a novel unrolled decoding algorithm for polar codes that enhances list decoding speed by an order of magnitude in software implementations.

Findings

Decoding speed improved by an order of magnitude.

Faster than the fastest LDPC decoders in software.

Achieves comparable error correction performance.

Abstract

Polar codes asymptotically achieve the symmetric capacity of memoryless channels, yet their error-correcting performance under successive-cancellation (SC) decoding for short and moderate length codes is worse than that of other modern codes such as low-density parity-check (LDPC) codes. Of the many methods to improve the error-correction performance of polar codes, list decoding yields the best results, especially when the polar code is concatenated with a cyclic redundancy check (CRC). List decoding involves exploring several decoding paths with SC decoding, and therefore tends to be slower than SC decoding itself, by an order of magnitude in practical implementations. In this paper, we present a new algorithm based on unrolling the decoding tree of the code that improves the speed of list decoding by an order of magnitude when implemented in software. Furthermore, we show that for software-defined radio applications, our proposed algorithm is faster than the fastest software implementations of LDPC decoders in the literature while offering comparable error-correction performance at similar or shorter code lengths.