Polynomial complexity of polar codes for non-binary alphabets, key agreement and Slepian-Wolf coding

TL;DR

This paper demonstrates that polar codes for non-binary sources, key agreement, and Slepian-Wolf coding can be constructed with polynomial complexity, extending previous results to more general settings and multi-user scenarios.

Contribution

It extends polynomial complexity results of polar codes to non-binary alphabets and multi-user problems, achieving optimal rates with manageable complexity.

Findings

Complexity is polynomial in the reciprocal of the gap to the rate limit.

Applicable to non-binary sources, key generation, and Slepian-Wolf coding.

Complexity scales well with the number of users.

Abstract

We consider polar codes for memoryless sources with side information and show that the blocklength, construction, encoding and decoding complexities are bounded by a polynomial of the reciprocal of the gap between the compression rate and the conditional entropy. This extends the recent results of Guruswami and Xia to a slightly more general setting, which in turn can be applied to (1) sources with non-binary alphabets, (2) key generation for discrete and Gaussian sources, and (3) Slepian-Wolf coding and multiple accessing. In each of these cases, the complexity scaling with respect to the number of users is also controlled. In particular, we construct coding schemes for these multi-user information theory problems which achieve optimal rates with an overall polynomial complexity.