Related papers: On Multiple Decoding Attempts for Reed-Solomon Cod…
We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…
Restricted Syndrome Decoding (ResSD) is a variant of linear code decoding problem where each of the error's entries must belong to a fixed small set of values. This problem underlies the security of CROSS, a post-quantum signature scheme…
The sum-rank metric is a hybrid between the Hamming metric and the rank metric and suitable for error correction in multishot network coding and distributed storage as well as for the design of quantum-resistant cryptosystems. In this work,…
For communication systems with heavy burst noise, an optimal Forward Error Correction (FEC) scheme is expected to have a large burst error correction capacity while simultaneously owning moderate random error correction capability. This…
Spatial modulation (SM) is a promising multiple-input multiple-output system used to increase spectral efficiency. The maximum likelihood (ML) decoder jointly detects the transmitted SM symbol, which is of high complexity. In this paper, a…
In this paper, we prove that the sub-field images of generalized Reed-Solomon (RS) codes can achieve the symmetric capacity of p-ary memoryless channels. Unlike the totally random linear code ensemble, as a class of maximum distance…
Long Reed-Solomon (RS) codes are desirable for digital communication and storage systems due to their improved error performance, but the high computational complexity of their decoders is a key obstacle to their adoption in practice. As…
Reed--Solomon error-correcting codes are ubiquitous across computer science and information theory, with applications in cryptography, computational complexity, communication and storage systems, and more. Most works on efficient error…
In lossy image compression, the objective is to achieve minimal signal distortion while compressing images to a specified bit rate. The increasing demand for visual analysis applications, particularly in classification tasks, has emphasized…
In the search for highly efficient decoders for short LDPC codes approaching maximum likelihood performance, a relayed decoding strategy, specifically activating the ordered statistics decoding process upon failure of a neural min-sum…
An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbol-wise function of a sequence available only at the encoder and a sequence that can be measured only at the decoder. This classical…
The classical majority-logic decoder proposed by Reed for Reed-Muller codes RM(r, m) of order r and length 2^m, unfolds in r+1 sequential steps, decoding message symbols from highest to lowest degree. Several follow-up decoding algorithms…
In this paper we survey the various erasure codes which had been proposed and patented recently, and along the survey we provide introductory tutorial on many of the essential concepts and readings in erasure and Fountain codes. Packet…
Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the…
The main computational steps in algebraic soft-decoding, as well as Sudan-type list-decoding, of Reed-Solomon codes are bivariate polynomial interpolation and factorization. We introduce a computational technique, based upon re-encoding and…
Sequential rate-distortion (SRD) theory provides a framework for studying the fundamental trade-off between data-rate and data-quality in real-time communication systems. In this paper, we consider the SRD problem for multi-dimensional…
Depth image based rendering techniques for multiview applications have been recently introduced for efficient view generation at arbitrary camera positions. Encoding rate control has thus to consider both texture and depth data. Due to…
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be…
Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve…
The Plotkin construction combines two codes to a code of doubled length. It can be applied recursively. The class of Reed-Muller (RM) codes is a particular example. Also, a special class of generalized concatenated codes (GCC) can be…