Belief Propagation List Decoding of Polar Codes

TL;DR

This paper introduces a belief propagation list decoder for polar codes that achieves near-ML performance, offers lower latency, and can be integrated with iterative detection, representing a significant advancement over traditional SCL decoding.

Contribution

The paper presents a novel belief propagation list decoding algorithm for polar codes that matches SCL performance without altering code structure and enables soft outputs for iterative decoding.

Findings

Achieves performance comparable to SCL decoding for polar codes.

Provides lower decoding latency and higher throughput potential.

Enhances error-rate performance with optimized frozen bit selection.

Abstract

We propose a belief propagation list (BPL) decoder with comparable performance to the successive cancellation list (SCL) decoder of polar codes, which already achieves the maximum likelihood (ML) bound of polar codes for sufficiently large list size $L$. The proposed decoder is composed of multiple parallel independent belief propagation (BP) decoders based on differently permuted polar code factor graphs. A list of possible transmitted codewords is generated and the one closest to the received vector, in terms of Euclidean distance, is picked. To the best of our knowledge, the proposed BPL decoder provides the best performance of plain polar codes under iterative decoding known so far. The proposed algorithm does not require any changes in the polar code structure itself, rendering the BPL into an alternative to the SCL decoder, equipped with a soft output capability enabling, e.g., iterative detection and decoding to further improve performance. Further benefits are lower decoding latency compared to the SCL decoder and the possibility of high throughput implementations. Additionally, we show that a different selection strategy of frozen bit positions can further enhance the error-rate performance of the proposed decoder.