Enhanced Successive Cancellation List Decoder for Long Polar Codes Targeting Air Interface

TL;DR

This paper introduces advanced decoding algorithms for long polar codes, significantly reducing memory and computational requirements while maintaining near-optimal performance for air interface applications.

Contribution

It proposes novel bias-enhanced and partitioned SCL decoders that improve efficiency and scalability for long polar codes, with theoretical performance analysis.

Findings

67% reduction in memory usage with similar decoding performance

Up to 5.4 times reduction in computational complexity

Negligible performance loss of 0.05 dB compared to larger list decoders

Abstract

Polar codes are the first codes with a proven capacity-achieving capability, but their decoding faces several challenges, especially under long code lengths. In this paper, we target algorithmic improvements and analyses to enable the implementation of long polar codes (e.g., length 8K bits) by addressing key challenges in memory usage and computational complexity presented by successive cancellation list (SCL) polar decoding. Perturbation-enhanced (PE) SCL decoders with a list size of $L$ reach the decoding performance of the SCL decoder with a list size of $2L$. The proposed bias-enhanced (BE) SCL decoders, which simplify the PE SCL decoder based on insights gained by an ablation study, return similar decoding performance to PE SCL decoders. Also, proposed BE generalized partitioned SCL (GPSCL) decoders with a list size of $8$ have a $67\%$ reduction in the memory usage and similar decoding performance compared to SCL decoders with a list size of $16$, and it demonstrates that an accurate bias can be generated under a reduced number of codewords from the list and reduces the overhead from $\left(L-1\right)n$ XOR gates plus $n$ priority encoders to $n$ XOR gates, where $n$ is the code length. Furthermore, input-distribution-aware (IDA) decoding is applied to BE GPSCL decoders, which shows how an accurate bias is generated under a low-complexity decoder. Up to $5.4\times$ reduction in the computational complexity is achieved compared to SCL decoders with a list size of $16$, and negligible latency overhead is added to the decoding process. The degraded decoding performance is at most $0.05\text{ dB}$ compared to BE GPSCL decoders without IDA decoding. Lastly, we theoretically prove that the bias in the BE SCL decoder moves the received soft information toward valid polar codewords with a high likelihood, and explain the decoding performance gain.