Asymmetric Construction of Low-Latency and Length-Flexible Polar Codes

TL;DR

This paper introduces an asymmetric polar coding scheme that enables arbitrary block lengths with lower decoding complexity, maintaining error correction performance comparable to existing methods, suitable for 5G applications.

Contribution

The paper proposes a novel asymmetric polar coding scheme that allows flexible code lengths with reduced decoding complexity compared to traditional length-matching techniques.

Findings

Achieves arbitrary block lengths for polar codes.

Reduces successive cancellation decoding operations by up to 50%.

Maintains similar error correction performance to existing schemes.

Abstract

Polar codes are a class of capacity-achieving error correcting codes that have been selected for use in enhanced mobile broadband in the 3GPP 5th generation (5G) wireless standard. Most polar code research examines the original Arikan polar coding scheme, which is limited in block length to powers of two. This constraint presents a considerable obstacle since practical applications call for all code lengths to be readily available. Puncturing and shortening techniques allow for flexible polar codes, while multi-kernel polar codes produce native code lengths that are powers of two and/or three. In this work, we propose a new low complexity coding scheme called asymmetric polar coding that allows for any arbitrary block length. We present details on the generator matrix, frozen set design, and decoding schedule. Our scheme offers flexible polar code lengths with decoding complexity lower than equivalent state-of-the-art length-compatible approaches under successive cancellation decoding. Further, asymmetric decoding complexity is directly dependent on the codeword length rather than the nearest valid polar code length. We compare our scheme with other length matching techniques, and simulations are presented. Results show that asymmetric polar codes present similar error correction performance to the competing schemes, while dividing the number of SC decoding operations by up to a factor of 2 using the same codeword length