Approaching the Finite Blocklength Capacity within 0.025dB by Short Polar Codes and CRC-Aided Hybrid Decoding

TL;DR

This paper demonstrates that short polar codes with CRC-aided hybrid decoding can nearly reach the finite blocklength capacity, achieving within 0.025dB at a block error ratio of 10^-3.

Contribution

The paper introduces a CRC-aided hybrid decoding algorithm that combines adaptive successive cancellation list decoding with sphere decoding to approach ML performance efficiently.

Findings

CA-HD achieves within 0.025dB of the finite blocklength capacity.

The hybrid decoding significantly improves performance over traditional methods.

Simulation results validate the effectiveness of the proposed approach.

Abstract

In this letter, we explore the performance limits of short polar codes and find that the maximum likelihood (ML) performance of a simple CRC-polar concatenated scheme can approach the finite blocklength capacity. Then, in order to approach the ML performance with a low average complexity, a CRC-aided hybrid decoding (CA-HD) algorithm is proposed and its decoding process is divided into two steps. In the first step, the received sequence is decoded by the adaptive successive cancellation list (ADSCL) decoding. In the second step, CRC-aided sphere decoding with a reasonable initial radius is used to decode the received sequence. To obtain the reasonable radius, the CRC bits of the survival paths in ADSCL are recalculated and the minimum Euclidean distance between the survival path and the received sequence is chosen as the initial radius. The simulation results show that CA-HD can achieve within about $0.025$dB of the finite blocklength capacity at the block error ratio $10^{-3}$ with code length $128$ and code rate $1/2$.