Decoding Analog Subspace Codes: Algorithms for Character-Polynomial Codes
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909249403092992 |
|---|---|
| author | Riasat, Samin Mahdavifar, Hessam |
| author_facet | Riasat, Samin Mahdavifar, Hessam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03606 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decoding Analog Subspace Codes: Algorithms for Character-Polynomial Codes Riasat, Samin Mahdavifar, Hessam Information Theory Signal Processing 94B35, 94B65 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. |
| title | Decoding Analog Subspace Codes: Algorithms for Character-Polynomial Codes |
| topic | Information Theory Signal Processing 94B35, 94B65 |
| url | https://arxiv.org/abs/2407.03606 |