We give a construction of quantum LDPC codes of dimension and distance as the code
length. Using a product of chain complexes this construction also provides a family of …

Spectral graph theory is the study and exploration of graphs through the eigenvalues and
eigenvectors of matrices naturally associated with those graphs. It is intuitively related to …

How can one exchange information e? ectively when the medium of com-nication introduces
errors? This question has been investigated extensively starting with the seminal works of …

We present an explicit construction of linear-time encodable and decodable codes of rate r
which can correct a fraction (1-r-/spl epsiv/)/2 of errors over an alphabet of constant size …

Combinatorial techniques have become essential tools across the landscape of
computational science, and some of the combinatorial ideas undergirding these tools are …

We show that for low-density parity-check (LDPC) codes whose Tanner graphs have
sufficient expansion, the linear programming (LP) decoder of Feldman, Karger, and …

Group-testing refers to the problem of identifying (with high probability) a (small) subset of D
defectives from a (large) set of N items via a “small” number of “pooled” tests (ie, tests that …

We derive lower bounds on the density of parity-check matrices of binary linear codes which
are used over memoryless binary-input output-symmetric (MBIOS) channels. The bounds …

We present an explicit construction of linear-time encodable and decodable codes of rate r
which can correct a fraction (1—r ε)/2 of errors over an alphabet of constant size depending …

The performance of punctured low-definition parity-check (LDPC) codes under maximum-
likelihood (ML) decoding is studied in this correspondence via deriving and analyzing their …