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Published in: Applicable Algebra in Engineering, Communication and Computing 2/2022

02-06-2020 | Original Paper

Multiple-rate error-correcting coding scheme

Authors: R. S. Raja Durai, Meenakshi Devi, Ashwini Kumar

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 2/2022

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Abstract

Error-correcting codes that can effectively encode and decode messages of distinct lengths while maintaining a constant blocklength are considered. It is known conventionally that a k-dimensional block code of length n defined over \(\texttt {GF}(q^{n})\) is designed to encode a k-symbol user data in to an n-length codeword, resulting in a fixed-rate coding. In contrast, considering \(q=p^{\lambda }\), this paper proposes two coding procedures (for the cases of \(\lambda =k\) and \(\lambda =n\)) each deriving a multiple-rate code from existing channel codes defined over a composite field \(\texttt {GF}(q^{n})\). Formally, the proposed coding schemes employ \(\lambda\) codes \({\mathcal {C}}_{1}(\lambda , 1), {\mathcal {C}}_{2}(\lambda , 2), \ldots , {\mathcal {C}}_{\lambda }(\lambda , \lambda )\) defined over \(\texttt {GF}(q)\) to encode user messages of distinct lengths and incorporate variable-rate feature. Unlike traditional block codes, the derived multiple-rate codes of fixed blocklength n can be used to encode and decode user messages \(\mathbf{m}\) of distinct lengths \(|\mathbf{m}| = 1, 2, \ldots , k, k+1, \ldots , kn\), thereby supporting a range of information rates—inclusive of the code rates \(1/n^{2}, 2/n^{2},\ldots , k/n^{2}\) and \(1/n, 2/n, \ldots , k/n\) ! A simple decoding procedure to the derived multiple-rate code is also given; in that, orthogonal projectors are employed for the identification of encoded user messages of variable length.
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Metadata
Title
Multiple-rate error-correcting coding scheme
Authors
R. S. Raja Durai
Meenakshi Devi
Ashwini Kumar
Publication date
02-06-2020
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 2/2022
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-020-00435-x

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