We present a method to construct low-density parity-check (LDPC) codes with low error
floors on the binary symmetric channel. Codes are constructed so that their Tanner graphs …

Linear programming (LP) decoding for low-density parity-check codes was introduced by
Feldman et al. and has been shown to have theoretical guarantees in several regimes …

Here we develop an approach to predict power grid weak points, and specifically to
efficiently identify the most probable failure modes in static load distribution for a given …

The goal of the present paper is the derivation of a framework for the finite-length analysis of
message-passing iterative decoding of low-density parity-check codes. To this end we …

In this paper, we develop a theoretical framework for the analysis and design of fault-tolerant
memory architectures. Our approach is a modification of the method developed by Taylor …

Alternating direction method of multipliers (ADMM) is an efficient implementation of linear
programming (LP) decoding for low-density parity-check (LDPC) codes. By adding penalty …

It is proven in this work that it is NP-complete to exhaustively enumerate small error-prone
substructures in arbitrary, finite-length low-density parity-check (LDPC) codes. Two error …

We describe a family of instanton-based optimization methods developed recently for the
analysis of the error floors of low-density parity-check (LDPC) codes. Instantons are the most …

We discuss the performance of low-density-parity-check (LDPC) codes decoded by means
of linear programming (LP) at moderate and large signal-to-noise-ratios (SNR). Utilizing a …

In linear programming (LP) decoding of a low-density parity-check (LDPC) code one
minimizes a linear functional, with coefficients related to log-likelihood ratios, over a …