Decoding Analog Subspace Codes: Algorithms for Character-Polynomial Codes
Samin Riasat, Hessam Mahdavifar
TL;DR
This work addresses decoding CP (character-polynomial) analog subspace codes for non-coherent communications by revealing their RS-subcode structure when the character is omitted. It develops minimum-distance decoding and Guruswami–Sudan list decoding adapted to CP codes, with a mapping step that ties CP decoding to RS decoding and a complexity analysis showing practical feasibility. The authors provide tight minimum-distance bounds, conditions under which CP is MDS, and a probabilistic analysis demonstrating significant average-list-size improvements due to CP’s subcode structure, supported by simulations. The results enable efficient, RS-based decoding of CP codes on analog operator channels, offering a path toward practical deployment and suggesting extensions to broader field settings, higher-dimensional CP codes, and soft-decision techniques.
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.