A Dynamic Programming Method to Construct Polar Codes with Improved Performance

TL;DR

This paper introduces a dynamic programming approach to polar code construction that optimizes performance under the SCL decoder, addressing the mismatch in reliability measures and achieving significant performance gains.

Contribution

It presents a novel DP-based method for constructing polar codes tailored for SCL decoding, improving upon standard reliability-based methods.

Findings

Achieves 0.3-1 dB performance improvement over standard polar codes

Optimizes information bit selection for different list sizes

Demonstrates consistent gains across various code lengths and rates

Abstract

In the standard polar code construction, the message vector $(U_0,U_1,\dots,U_{n-1})$ is divided into information bits and frozen bits according to the reliability of each $U_i$ given $(U_0,U_1,\dots,U_{i-1})$ and all the channel outputs. While this reliability function is the most suitable measure to choose information bits under the Successive Cancellation (SC) decoder, there is a mismatch between this reliability function and the Successive Cancellation List (SCL) decoder because the SCL decoder also makes use of the information from the future frozen bits. We propose a Dynamic Programming (DP) construction of polar codes to resolve this mismatch. Our DP construction chooses different sets of information bits for different list sizes in order to optimize the performance of the constructed code under the SCL decoder. Simulation results show that our DP-polar codes consistently demonstrate $0.3$--$1$dB improvement over the standard polar codes under the SCL decoder with list size $32$ for various choices of code lengths and code rates.