Decoding Analog Subspace Codes: Algorithms for Character-Polynomial Codes

TL;DR

This paper introduces efficient decoding algorithms for character-polynomial codes, a class of analog subspace codes, by leveraging their relationship with Reed-Solomon codes and classical decoding techniques.

Contribution

It presents novel decoding algorithms for CP codes and demonstrates how classical RS decoding methods can be adapted for these codes, including probabilistic analysis of list decoding improvements.

Findings

Decoding algorithms for CP codes are efficient and leverage RS decoding methods.

In most cases, list decoding of CP codes behaves as a unique decoding.

Probabilistic analysis shows improved list decoding performance for CP codes.

Abstract

We propose efficient minimum-distance decoding and list-decoding algorithms for a certain class of analog subspace codes, referred to as character-polynomial (CP) codes, recently introduced by Soleymani and the second author. In particular, a CP code without its character can be viewed as a subcode of a Reed-Solomon (RS) code, where a certain subset of the coefficients of the message polynomial is set to zeros. We then demonstrate how classical decoding methods, including list decoders, for RS codes can be leveraged for decoding CP codes. For instance, it is shown that, in almost all cases, the list decoder behaves as a unique decoder. We also present a probabilistic analysis of the improvements in list decoding of CP codes when leveraging their certain structure as subcodes of RS codes.