On the Message Passing Efficiency of Polar and Low-Density Parity-Check Decoders

TL;DR

This paper analyzes message-passing decoding algorithms for polar and LDPC codes, revealing that successive cancellation decoding is more efficient than belief propagation despite weaker error correction, through complexity-performance tradeoff analysis.

Contribution

It provides a new message-by-message analysis of decoding efficiency, highlighting the surprising effectiveness of SC decoding and offering insights into scheduling strategies.

Findings

SC decoding has higher efficiency than BP in message-passing framework.

Complexity measured by number of messages passed correlates with decoding efficiency.

Results support recent high-speed polar SC decoder implementations.

Abstract

This study focuses on the efficiency of message-passing-based decoding algorithms for polar and low-density parity-check (LDPC) codes. Both successive cancellation (SC) and belief propagation (BP) decoding algorithms are studied {in} the message-passing framework. Counter-intuitively, SC decoding demonstrates the highest decoding efficiency, although it was considered a weak decoder {in terms of} error-correction performance. We analyze the complexity-performance tradeoff to dynamically track the decoding efficiency, where the complexity is measured by the number of messages passed (NMP), and the performance is measured by the statistical distance to the maximum a posteriori (MAP) estimate. This study offers a new insight into the contribution of each message passed in decoding, and compares various decoding algorithms on a message-by-message level. The analysis corroborates recent results on terabits-per-second polar SC decoders, and might shed light on better scheduling strategies.