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The glassy phase of Gallager codes
UMR 8549, Unit′e Mixte de Recherche du Centre National de la Recherche Scientifi que et de l’ Ecole Normale Sup′erieure
2015/8/21
Gallager codes are the best error-correcting codes to-date. In this paper we study them by using the tools of statistical mechanics. The corresponding statistical mechanics model is a spin model on a ...
How to Find Good Finite-Length Codes: From Art Towards Science
LDPC coding transmission binary probability
2015/8/21
We explain how to optimize finite-length LDPC codes for transmission over the binary erasure channel. Our approach relies on an analytic approximation of the erasure probability. This is in turn...
Binomial coefficient codes over GF
Graham, binomial coefficient coding, discrete mathematics, number of codewords, industry convergence rate
2015/7/14
Diaconis, P. and R. Graham, Binomial coefficient codes over GF(2) Discrete Mathematics
106/107 (1992) 181-188.
In this note we study codes over GF(2) which are generated for given d and r by binar...
Gray codes for randomization procedurse.
The Sorting Index and Permutation Codes
permutation statistic Mahonian statistic Coxeter group set-valued statistic bijection
2014/6/3
In the combinatorial study of the coefficients of a bivariate polynomial that generalizes both the length and the reflection length generating functions for finite Coxeter groups, Petersen introduced ...
The Sorting Index and Permutation Codes
Permutation statistics Mahonian statistics Coxeter groups Set-valued statistics Bijections
2012/6/19
In the combinatorial study of the coefficients of a bivariate polynomial that generalizes both the length and the reflection length generating functions for finite Coxeter groups, Petersen introduced ...
Expander Graph Based Overlapped Chunked Codes
Expander Graph Based Overlapped Chunked Codes
2012/12/4
Chunked codes are a variation of random linear network codes with low computational complexities. In chunked codes, the packets in a file are grouped into small (non-overlapped or overlapped) chunks, ...
Tree Codes Improve Convergence Rate of Consensus Over Erasure Channels
Tree Codes Convergence Rate of Consensus Erasure Channels Optimization and Control
2012/4/17
We study the problem of achieving average consensus between a group of agents over a network with erasure links. In the context of consensus problems, the unreliability of communication links between ...
We describe two different approaches to making systematic classifications of plane lattice polygons, and recover the toric codes they generate, over small fields, where these match or exceed the best ...
Quaternary Constant-Composition Codes with Weight Four and Distances Five or Six
Quaternary Constant-Composition Codes Weight Four Distances Five or Six
2012/3/1
The sizes of optimal constant-composition codes of weight three have been determined by Chee, Ge and Ling with four cases in doubt. Group divisible codes played an important role in their construction...
国家杰出青年科学基金获得者葛根年:Combinatorial codes--A survey
国家 杰出青年 科学基金 葛根年 Combinatorial codes A survey
2012/1/5
Combinatorial designs have close connections with coding theory. In this talk, I will give a survey on combinatorial codes which were studied in the combinatorial community of China. These include: o...
Abstract: The existence question for tiling of the $n$-dimensional Euclidian space by crosses is well known. A few existence and nonexistence results are known in the literature. Of special interest a...
On the vanishing ideal of an algebraic toric set and its parameterized linear codes
algebraic toric set parameterized linear codes Commutative Algebra
2011/9/16
Abstract: Let K be a finite field and let X be a subset of a projective space, over the field K, which is parameterized by monomials arising from the edges of a clutter. We show some estimates for the...
Abstract: In this paper we define homological stabilizer codes which encompass codes such as Kitaev's toric code and the topological color codes. These codes are defined solely by the graphs they resi...
An algorithm for list decoding number field codes
algorithm number field codes Number Theory
2011/9/5
Abstract: We present an algorithm for list decoding codewords of algebraic number field codes in polynomial time. This is the first explicit procedure for decoding number field codes whose constructio...