相关论文: Maximum-likelihood decoding of Reed-Solomon Codes …

The maximum-likelihood decoding problem is known to be NP-hard for general linear and Reed-Solomon codes. In this paper, we introduce the notion of A-covered codes, that is, codes that can be decoded through a polynomial time algorithm A…

The minimum distance is one of the most important combinatorial characterizations of a code. The maximum likelihood decoding problem is one of the most important algorithmic problems of a code. While these problems are known to be hard for…

Establishing the complexity of {\em Bounded Distance Decoding} for Reed-Solomon codes is a fundamental open problem in coding theory, explicitly asked by Guruswami and Vardy (IEEE Trans. Inf. Theory, 2005). The problem is motivated by the…

The complexity of maximal likelihood decoding of the Reed-Solomon codes $[q-1, k]_q$ is a well known open problem. The only known result in this direction states that it is at least as hard as the discrete logarithm in some cases where the…

Maximum-likelihood (ML) decoding for arbitrary block codes remains fundamentally hard, with worst-case time complexity-measured by the total number of multiplications-being no better than straightforward exhaustive search, which requires…

In this paper we address the problem of decoding linearized Reed-Solomon (LRS) codes beyond their unique decoding radius. We analyze the complexity in order to evaluate if the considered problem is of cryptographic relevance, i.e., can be…

Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to…

In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the…

Starting from a practical use of Reed-Solomon codes in a cryptographic scheme published in Indocrypt'09, this paper deals with the threshold of linear $q$-ary error-correcting codes. The security of this scheme is based on the…

A complexity-adaptive tree search algorithm is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding by using a successive decoding schedule. The average complexity is close to that of the successive…

Reed-Solomon codes are a classic family of error-correcting codes consisting of evaluations of low-degree polynomials over a finite field on some sequence of distinct field elements. They are widely known for their optimal unique-decoding…

The computational complexity of the Maximum Likelihood decoding algorithm in [1], [2] for orthogonal space-time block codes is smaller than specified.

A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making…

In this paper show that the list and bounded-distance decoding problems of certain bounds for the Reed-Solomon code are at least as hard as the discrete logarithm problem over finite fields.

Since the classical work of Berlekamp, McEliece and van Tilborg, it is well known that the problem of exact maximum-likelihood (ML) decoding of general linear codes is NP-hard. In this paper, we show that exact ML decoding of a classs of…

A novel and efficient neural decoder algorithm is proposed. The proposed decoder is based on the neural Belief Propagation algorithm and the Automorphism Group. By combining neural belief propagation with permutations from the Automorphism…

Recursive list decoding is considered for Reed-Muller (RM) codes. The algorithm repeatedly relegates itself to the shorter RM codes by recalculating the posterior probabilities of their symbols. Intermediate decodings are only performed…

An efficient decoder for the generalized first-order Reed-Muller code RM_q(1,m) is essential for the decoding of various block-coding schemes for orthogonal frequency-division multiplexing with reduced peak-to-mean power ratio. We present…

We investigate the list decodability of symbol-pair codes in the present paper. Firstly, we show that list decodability of every symbol-pair code does not exceed the Gilbert-Varshamov bound. On the other hand, we are able to prove that with…

This paper considers the average complexity of maximum likelihood (ML) decoding of convolutional codes. ML decoding can be modeled as finding the most probable path taken through a Markov graph. Integrated with the Viterbi algorithm (VA),…