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.

翻译：我们针对一类特定的模拟子空间码——即由Soleymani与第二作者最近提出的字符多项式（CP）码——提出了高效的最小距离解码和列表解码算法。具体而言，不带字符的CP码可视为Reed-Solomon（RS）码的一个子码，其中消息多项式的特定系数子集被设为零。随后，我们展示了如何利用RS码的经典解码方法（包括列表解码器）来解码CP码。例如，研究表明在几乎所有情况下，列表解码器表现为唯一解码器。我们还通过概率分析，探讨了利用CP码作为RS码子码的特定结构对其列表解码性能的改进。