Related papers: New Results on the Pseudoredundancy
Let C be a linear code with length n and minimum distance d. The stopping redundancy of C is defined as the minimum number of rows in a parity-check matrix for C such that the smallest stopping sets in the corresponding Tanner graph have…
In this paper, an idea of the cutting plane method is employed to improve the fractional distance of a given binary parity check matrix. The fractional distance is the minimum weight (with respect to l1-distance) of vertices of the…
The study of linear codes over a finite field of odd cardinality, derived from determinantal varieties obtained from symmetric matrices of bounded rank, was initiated in a recent paper by the authors. There, one found the minimum distance…
This paper defines a new pseudometric for binary relations between finite sets that measures consensus among subsets. The main results are (1) a concise restatement of this pseudometric with an intuitively appealing interpretation via a…
A non-binary (2,v)-regular LDPC code is defined by a parity-check matrix with column weight 2 and row weight v. In this report, we give an ontology-based approach to the optimization for this class of codes. All possible inter-connected…
[Draft] In this paper, the redundancy of Slepian Wolf coding is revisited. Applying the random binning and converse technique in \cite{yang}, the same results in \cite{he} are obtained with much simpler proofs. Moreover, our results reflect…
In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum…
We present a method for estimating the undetected error rate when a cyclic redundancy check (CRC) is performed on the output of the decoder of short low-density parity-check (LDPC) codes. This system is of interest for telecommand links,…
Consider the set of source distributions within a fixed maximum relative entropy with respect to a given nominal distribution. Lossless source coding over this relative entropy ball can be approached in more than one way. A problem…
We study the performance of nonbinary low-density parity-check (LDPC) codes over finite integer rings over two channels that arise from the Lee metric. The first channel is a discrete memory-less channel (DMC) matched to the Lee metric. The…
Pseudo-labeling is a commonly used paradigm in semi-supervised learning, yet its application to semi-supervised regression (SSR) remains relatively under-explored. Unlike classification, where pseudo-labels are discrete and confidence-based…
In this paper we show the usability of the Gray code with constant weight words for computing linear combinations of codewords. This can lead to a big improvement of the computation time for finding the minimum distance of a code. We have…
We derive bounds on the asymptotic density of parity-check matrices and the achievable rates of binary linear block codes transmitted over memoryless binary-input output-symmetric (MBIOS) channels. The lower bounds on the density of…
Iterative decoding and linear programming decoding are guaranteed to converge to the maximum-likelihood codeword when the underlying Tanner graph is cycle-free. Therefore, cycles are usually seen as the culprit of low-density parity-check…
The linear programming decoder will occasionally output fractional-valued sequences that do not correspond to binary codewords - such outputs are termed nontrivial pseudocodewords. Feldman et al. have demonstrated that it is precisely the…
Existence of quantum low-density parity-check (LDPC) codes whose minimal distance scales linearly with the number of qubits is a major open problem in quantum information. Its practical interest stems from the need to protect information in…
Belief Propagation (BP) and Linear Programming (LP) decodings of Low Density Parity Check (LDPC) codes are discussed. We summarize results of instanton/pseudo-codeword approach developed for analysis of the error-floor domain of the codes.…
This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…
In recent years, several integer programming (IP) approaches were developed for maximum-likelihood decoding and minimum distance computation for binary linear codes. Two aspects in particular have been demonstrated to improve the…
The minimum average number of bits need to describe a random variable is its entropy, assuming knowledge of the underlying statistics On the other hand, universal compression supposes that the distribution of the random variable, while…