This article is focused on the performance evaluation of linear codes under optimal
maximum-likelihood (ML) decoding. Though the ML decoding algorithm is prohibitively …

We present a novel framework for applying deep neural networks (DNN) to soft decoding of
linear codes at arbitrary block lengths. Unlike other approaches, our framework allows …

This paper investigates decoding of low-density parity-check (LDPC) codes over the binary
erasure channel (BEC). We study the iterative and maximum-likelihood (ML) decoding of …

We present two sequences of ensembles of nonsystematic irregular repeat-accumulate
(IRA) codes which asymptotically (as their block length tends to infinity) achieve capacity on …

A new method for analyzing low-density parity-check (LDPC) codes and low-density
generator-matrix (LDGM) codes under bit maximum a posteriori probability (MAP) decoding …

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 …

There is a fundamental relationship between belief propagation (BP) and maximum a
posteriori decoding. The case of transmission over the binary erasure channel was …

Extreme densities for information combining are found for two important channel models: the
binary-input symmetric parallel broadcast channel and the parity-constrained-input …

We determine the rank of a random matrix A over an arbitrary field with prescribed numbers
of non-zero entries in each row and column. As an application we obtain a formula for the …

Using combinatorial arguments, we determine an upper bound on achievable rates of
stabilizer codes used over the quantum erasure channel. This allows us to recover the no …