Compound Polar Codes

TL;DR

This paper introduces a unified polar coding scheme for multi-channel communication that achieves capacity with a single encoder and decoder, improving error performance over traditional separate schemes.

Contribution

It proposes a novel compound polar coding scheme that simplifies implementation and achieves capacity over multi-channels, with demonstrated finite-length performance improvements.

Findings

Achieves capacity over multi-channels with a single encoder and decoder.

Shows significant error probability reduction compared to separated schemes.

Validates performance improvements through numerical analysis and simulations.

Abstract

A capacity-achieving scheme based on polar codes is proposed for reliable communication over multi-channels which can be directly applied to bit-interleaved coded modulation schemes. We start by reviewing the ground-breaking work of polar codes and then discuss our proposed scheme. Instead of encoding separately across the individual underlying channels, which requires multiple encoders and decoders, we take advantage of the recursive structure of polar codes to construct a unified scheme with a single encoder and decoder that can be used over the multi-channels. We prove that the scheme achieves the capacity over this multi-channel. Numerical analysis and simulation results for BICM channels at finite block lengths shows a considerable improvement in the probability of error comparing to a conventional separated scheme.