Parameters of Codes for the Binary Asymmetric Channel

Asymmetric Binary Covering Codes

An asymmetric binary covering code of length n and radius R is a subset C of the n-cube Qn such that every vector x ∈ Qn can be obtained from some vector c ∈ C by changing at most R 1’s of c to 0’s, where R is as small as possible. K(n,R) is defined as the smallest size of such a code. We show K(n,R) ∈ Θ(2/n) for constant R, using an asymmetric sphere-covering bound and probabilistic methods. W...

Lattice Codes for the Binary Deletion Channel

The construction of deletion codes for the Levenshtein metric is reduced to the construction of codes over the integers for the Manhattan metric by run length coding. The latter codes are constructed by expurgation of translates of lattices. These lattices, in turn, are obtained from Construction A applied to binary codes and Z4−codes. A lower bound on the size of our codes for the Manhattan di...

The Metric Structure of Codes for the Binary Symmetric Channel

Superimposed codes for the multiaccess binary adder channel

P. Mathys, " A class of codes for a T active users out of N multiple-access communication system, " IEEE Trans. Error-correcting codes for a T-user binary adder channel, " ZEEE Trans. AbsiractSuperimposed codes for multiple-access communication in a binary adder channel are analyzed. The superposition mechanism used in this correspondence is ordinary addition. Each user is assigned a codeword f...

Gallager error-correcting codes for binary asymmetric channels

Abstract. We derive critical noise levels for Gallager codes on asymmetric channels as a function of the input bias and the temperature. Using a statistical mechanics approach we study the space of codewords and the entropy in the various decoding regimes. We further discuss the relation of the convergence of the message passing algorithm with the endogenous property and complexity, characteriz...