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Generic Decoding in the Sum-Rank Metric.

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Název: Generic Decoding in the Sum-Rank Metric.
Autoři: Puchinger, Sven1 mail@svenpuchinger.de, Renner, Julian2 julian.renner@tum.de, Rosenkilde, Johan1 jsrn@jsrn.dk
Zdroj: IEEE Transactions on Information Theory. Aug2022, Vol. 68 Issue 8, p5075-5097. 23p.
Témata: *DECODING algorithms, *LINEAR codes, *HARDNESS, *GENERIC drugs, *COMPLEXITY (Philosophy)
Geografický termín: EUROPE
Abstrakt: We propose the first non-trivial generic decoding algorithm for codes in the sum-rank metric. The new method combines ideas of well-known generic decoders in the Hamming and rank metric. For the same code parameters and number of errors, the new generic decoder has a larger expected complexity than the known generic decoders for the Hamming metric and smaller than the known rank-metric decoders. Furthermore, we give a formal hardness reduction, providing evidence that generic sum-rank decoding is computationally hard. As a by-product of the above, we solve some fundamental coding problems in the sum-rank metric: we give an algorithm to compute the exact size of a sphere of a given sum-rank radius, and also give an upper bound as a closed formula; and we study erasure decoding with respect to two different notions of support. [ABSTRACT FROM AUTHOR]
Databáze: Academic Search Index
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Abstrakt:We propose the first non-trivial generic decoding algorithm for codes in the sum-rank metric. The new method combines ideas of well-known generic decoders in the Hamming and rank metric. For the same code parameters and number of errors, the new generic decoder has a larger expected complexity than the known generic decoders for the Hamming metric and smaller than the known rank-metric decoders. Furthermore, we give a formal hardness reduction, providing evidence that generic sum-rank decoding is computationally hard. As a by-product of the above, we solve some fundamental coding problems in the sum-rank metric: we give an algorithm to compute the exact size of a sphere of a given sum-rank radius, and also give an upper bound as a closed formula; and we study erasure decoding with respect to two different notions of support. [ABSTRACT FROM AUTHOR]
ISSN:00189448
DOI:10.1109/TIT.2022.3167629