Rank-Metric Codes Over Finite Principal Ideal Rings and Applications

Kamche, Hermann Tchatchiem; Mouaha, Christophe

doi:10.1109/tit.2019.2933520

Cited by 24 publications

(74 citation statements)

References 76 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The simplified bound (14) in Theorem 5 coincides up to a constant with the bound by Gaborit et at. [10] in the case of a finite field (Galois ring with r = 1).…”

Section: Theorem 5 Let F Be Defined As In Defintion 2 Such That It Hasupporting

confidence: 74%

“…Network coding over certain finite rings was intensively studied in [ 7 , 11 ], motivated by works on nested-lattice-based network coding [ 8 , 18 , 26 , 28 ] which show that network coding over finite rings may result in more efficient physical-layer network coding schemes. Kamche et al [ 14 ] showed how lifted rank-metric codes over finite rings can be used for error correction in network coding. The result uses a similar approach as [ 23 ] to transformation the channel output into a rank-metric error-erasure decoding problem.…”

Section: Introductionmentioning

confidence: 99%

“…It was first shown in [ 15 ] how to construct space-time codes with optimal rate-diversity tradeoff via a rank-preserving mapping from rank-metric codes over Galois rings. This result was generalized to arbitrary finite principal ideal rings in [ 14 ]. The use of finite rings instead of finite fields has advantages since the rank-preserving mapping can be chosen more flexibly.…”

Section: Introductionmentioning

confidence: 99%

“…Kamche et al also defined and extensively studied Gabidulin codes over finite principal ideal rings. In particular, they proposed a Welch–Berlekamp-like decoder for Gabidulin codes and a Gröbner-basis-based decoder for interleaved Gabidulin codes [ 14 ].…”

Section: Introductionmentioning

confidence: 99%

“…For errors, the success probability is already and for , it is . A Gabidulin code as in [ 14 ], over the same ring and the same parameters, can correct any error of rank up to 30 (i.e., the same maximal radius). However, the currently fastest decoder for Gabidulin codes over rings [ 14 ] has a larger complexity than the LRPC decoder in Sect.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Low-rank parity-check codes over Galois rings

Renner

Neri

Puchinger

2020

Des. Codes Cryptogr.

View full text Add to dashboard Cite

Low-rank parity-check (LRPC) codes are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (Proceedings of the workshop on coding and cryptography WCC, vol 2013, 2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et al. (IEEE Trans Inf Theory 65(12):7718–7735, 2019), we define and study LRPC codes over Galois rings—a wide class of finite commutative rings. We give a decoding algorithm similar to Gaborit et al.’s decoder, based on simple linear-algebraic operations. We derive an upper bound on the failure probability of the decoder, which is significantly more involved than in the case of finite fields. The bound depends only on the rank of an error, i.e., is independent of its free rank. Further, we analyze the complexity of the decoder. We obtain that there is a class of LRPC codes over a Galois ring that can decode roughly the same number of errors as a Gabidulin code with the same code parameters, but faster than the currently best decoder for Gabidulin codes. However, the price that one needs to pay is a small failure probability, which we can bound from above.

show abstract

“…The simplified bound (14) in Theorem 5 coincides up to a constant with the bound by Gaborit et at. [10] in the case of a finite field (Galois ring with r = 1).…”

Section: Theorem 5 Let F Be Defined As In Defintion 2 Such That It Hasupporting

confidence: 74%