Study of Adaptive Reweighted Sparse Belief Propagation Decoders for Polar Codes

TL;DR

This work addresses the need for low-latency, high-performance decoding of polar codes. It introduces AR-SBP, an adaptive reweighted belief propagation decoder that refines LLR messages by an edge-dependent factor $\\rho$, governed by parameters $\\beta$ and $\\Delta$, and shows convergence under Roosta-style conditions. The paper provides a convergence analysis and complexity assessment, demonstrating that AR-SBP can outperform standard BP and SC with substantially fewer iterations, and approach NW-RBP and SCL performance at a fraction of the computational cost. Simulations on AWGN channels confirm faster convergence and competitive error-rate performance, highlighting the practical potential for low-latency polar-code applications.

Abstract

In this paper, we present an adaptive reweighted sparse belief propagation (AR-SBP) decoder for polar codes. The AR-SBP technique is inspired by decoders that employ the sum-product algorithm for low-density parity-check codes. In particular, the AR-SBP decoding strategy introduces reweighting of the exchanged log-likelihood-ratio in order to refine the message passing, improving the performance of the decoder and reducing the number of required iterations. An analysis of the convergence of AR-SBP is carried out along with a study of the complexity of the analyzed decoders. Numerical examples show that the AR-SBP decoder outperforms existing decoding algorithms for a reduced number of iterations, enabling low-latency applications.

Figures (3)

• Figure 1: Tanner graph and parity check matrix H
• Figure 2: BER versus iterations for BP, AR-SBP and NW-RBP.
• Figure 3: Polar codes performance for $N=256$ and $R=1/2$, for BP, AR-SBP and SCL, for $\text{T}_{max}$=60, $\text{T}_{max}$=20 and $\mathcal{L}$=128, respectively.