Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/30499
Title: | A matrix based list decoding algorithm for linear codes over integer residue rings |
Author: | Napp, Diego Pinto, Raquel Saçıkara, Elif Toste, Marisa |
Keywords: | Finite rings Linear codes over finite rings Erasure channel Decoding algorithms Matrix representations Parity-check matrix |
Issue Date: | 1-Apr-2021 |
Publisher: | Elsevier |
Abstract: | In this paper we address the problem of list decoding of linear codes over an integer residue ring Zq, where q is a power of a prime p. The proposed procedure exploits a particular matrix representation of the linear code over Zpr , called the standard form, and the p-adic expansion of the to-be-decoded vector. In particular, we focus on the erasure channel in which the location of the errors is known. This problem then boils down to solving a system of linear equations with coefficients in Zpr . From the parity-check matrix representations of the code we recursively select certain equations that a codeword must satisfy and have coefficients only in the field p^{r−1}Zpr . This yields a step by step procedure obtaining a list of the closest codewords to a given received vector with some of its coordinates erased. We show that such an algorithm actually computes all possible erased coordinates, that is, the provided list is minimal. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/30499 |
DOI: | 10.1016/j.laa.2020.09.031 |
ISSN: | 0024-3795 |
Appears in Collections: | CIDMA - Artigos DMat - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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List_Decoding_Revised_Version_FINAL.pdf | 284.24 kB | Adobe PDF | View/Open |
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