Related papers: New Decoding of Reed-Solomon Codes Based on FFT an…
This paper deals with the application of list decoding of Reed--Solomon codes to a concatenated code for key reproduction using Physical Unclonable Functions. The resulting codes achieve a higher error-correction performance at the same…
In this paper, Sphere Decoding (SD) algorithms for Spatial Modulation (SM) are developed to reduce the computational complexity of Maximum-Likelihood (ML) detectors. Two SDs specifically designed for SM are proposed and analysed in terms of…
The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a scenario where the sender transmits a codeword from some codebook, and the receiver obtains $N$ noisy outputs of the codeword. We study the problem of…
In the last years, Regev's reduction has been used as a quantum algorithmic tool for providing a quantum advantage for variants of the decoding problem. Following this line of work, the authors of [JSW+24] have recently come up with a…
This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels.…
Rate-Splitting Multiple Access (RSMA) has been recognized as a promising multiple access technique. We propose a novel architecture for downlink RSMA, namely Codeword-Segmentation RSMA (CS-RSMA). Different from conventional RSMA which…
Lifted Reed-Solomon and multiplicity codes are classes of codes, constructed from specific sets of $m$-variate polynomials. These codes allow for the design of high-rate codes that can recover every codeword or information symbol from many…
In this work, maximum sum-rank distance (MSRD) codes and linearized Reed-Solomon codes are extended to finite chain rings. It is proven that linearized Reed-Solomon codes are MSRD over finite chain rings, extending the known result for…
In this paper, we consider the application of Reed- Solomon (RS) channel coding for joint error correction and cooperative network coding on non-binary phase shift keying (PSK) modulated signals. The relay first decodes the RS channel coded…
Linearized Reed-Solomon (LRS) codes are sum-rank metric codes that fulfill the Singleton bound with equality. In the two extreme cases of the sum-rank metric, they coincide with Reed-Solomon codes (Hamming metric) and Gabidulin codes (rank…
MDS codes have garnered significant attention due to their wide applications in practice. To date, most known MDS codes are equivalent to Reed-Solomon codes. The construction of non-Reed-Solomon (non-RS) type MDS codes has emerged as an…
Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an…
Lifted Reed-Solomon codes, a subclass of lifted affine-invariant codes, have been shown to be of high rate while preserving locality properties similar to generalized Reed-Muller codes, which they contain as subcodes. This work introduces a…
Deep holes play an important role in the decoding of generalized Reed-Solomon codes. Recently, Wu and Hong \cite{WH} found a new class of deep holes for standard Reed-Solomon codes. In the present paper, we give a concise method to obtain a…
We present an algorithm for systematic encoding of Hermitian codes. For a Hermitian code defined over GF(q^2), the proposed algorithm achieves a run time complexity of O(q^2) and is suitable for VLSI implementation. The encoder architecture…
A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…
We propose efficient minimum-distance decoding and list-decoding algorithms for a certain class of analog subspace codes, referred to as character-polynomial (CP) codes, recently introduced by Soleymani and the second author. In particular,…
Algebraic codes that achieve list decoding capacity were recently constructed by a careful ``folding'' of the Reed-Solomon code. The ``low-degree'' nature of this folding operation was crucial to the list decoding algorithm. We show how…
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…
In this paper, we propose a new subcarrier index modulation scheme for orthogonal frequency division multiplexing (OFDM), which incorporates the Reed-Solomon (RS) encoding in a visible light communication (VLC) system. In this scheme, the…