169,437 research outputs found
New Combinatorial Construction Techniques for Low-Density Parity-Check Codes and Systematic Repeat-Accumulate Codes
This paper presents several new construction techniques for low-density
parity-check (LDPC) and systematic repeat-accumulate (RA) codes. Based on
specific classes of combinatorial designs, the improved code design focuses on
high-rate structured codes with constant column weights 3 and higher. The
proposed codes are efficiently encodable and exhibit good structural
properties. Experimental results on decoding performance with the sum-product
algorithm show that the novel codes offer substantial practical application
potential, for instance, in high-speed applications in magnetic recording and
optical communications channels.Comment: 10 pages; to appear in "IEEE Transactions on Communications
p-Adic estimates of Hamming weights in Abelian codes over Galois rings
A generalization of McEliece's theorem on the p-adic valuation of Hamming weights of words in cyclic codes is proved in this paper by means of counting polynomial techniques introduced by Wilson along with a technique known as trace-averaging introduced here. The original theorem of McEliece concerned cyclic codes over prime fields. Delsarte and McEliece later extended this to Abelian codes over finite fields. Calderbank, Li, and Poonen extended McEliece's original theorem to cover cyclic codes over the rings /spl Zopf//sub 2//sup d/, Wilson strengthened their results and extended them to cyclic codes over /spl Zopf//sub p//sup d/, and Katz strengthened Wilson's results and extended them to Abelian codes over /spl Zopf//sub p//sup d/. It is natural to ask whether there is a single analogue of McEliece's theorem which correctly captures the behavior of codes over all finite fields and all rings of integers modulo prime powers. In this paper, this question is answered affirmatively: a single theorem for Abelian codes over Galois rings is presented. This theorem contains all previously mentioned results and more
Numerical and analytical bounds on threshold error rates for hypergraph-product codes
We study analytically and numerically decoding properties of finite rate
hypergraph-product quantum LDPC codes obtained from random (3,4)-regular
Gallager codes, with a simple model of independent X and Z errors. Several
non-trival lower and upper bounds for the decodable region are constructed
analytically by analyzing the properties of the homological difference, equal
minus the logarithm of the maximum-likelihood decoding probability for a given
syndrome. Numerical results include an upper bound for the decodable region
from specific heat calculations in associated Ising models, and a minimum
weight decoding threshold of approximately 7%.Comment: 14 pages, 5 figure
Computation of conservation laws for nonlinear lattices
An algorithm to compute polynomial conserved densities of polynomial
nonlinear lattices is presented. The algorithm is implemented in Mathematica
and can be used as an automated integrability test. With the code diffdens.m,
conserved densities are obtained for several well-known lattice equations. For
systems with parameters, the code allows one to determine the conditions on
these parameters so that a sequence of conservation laws exist.Comment: To appear in Physica D, 17 pages, Latex, uses the style files
elsart.sty and elsart12.st
- …