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We introduce a new method for decoding short and moderate length linear block codes with dense parity-check matrix representations of cyclic form, termed multiple-bases belief-propagation (MBBP). The proposed iterative scheme makes use of…
Expectation Propagation is a generalization to Belief Propagation (BP) in two ways. First, it can be used with any exponential family distribution over the cliques in the graph. Second, it can impose additional constraints on the marginal…
A method for estimating the performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms on binary symmetric channels (BSC) is proposed. Based on the enumeration of the smallest weight error…
Block-fading (BF) channel, also known as slow-fading channel, is a type of simple and practical channel model that can characterize the primary feature of a number of wireless-communication applications with low to moderate mobility.…
We show that the performance of iterative belief propagation (BP) decoding of polar codes can be enhanced by decoding over different carefully chosen factor graph realizations. With a genie-aided stopping condition, it can achieve the…
For finite length polar codes, channel polarization leaves a significant number of channels not fully polarized. Adding a Cyclic Redundancy Check (CRC) to better protect information on the semi-polarized channels has already been…
Low-density parity-check (LDPC) codes have been successfully commercialized in communication systems due to their strong error correction capabilities and simple decoding process. However, the error-floor phenomenon of LDPC codes, in which…
We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. Second, we present an…
Classical low-density parity-check (LDPC) codes are a widely deployed and well-established technology, forming the backbone of modern communication and storage systems. It is well known that, in this classical setting, increasing the girth…
We describe and analyze the joint source/channel coding properties of a class of sparse graphical codes based on compounding a low-density generator matrix (LDGM) code with a low-density parity check (LDPC) code. Our first pair of theorems…
Low-density parity-check (LDPC) coding for a multitude of equal-capacity channels is studied. First, based on numerous observations, a conjecture is stated that when the belief propagation decoder converges on a set of equal-capacity…
To alleviate the suboptimal performance of belief propagation (BP) decoding of short low-density parity-check (LDPC) codes, a plethora of improved decoding algorithms has been proposed over the last two decades. Many of these methods can be…
One of the challenges often faced with wireless communication systems is its limited range and data-rate. Distributed Transmit Beamforming (DTB) techniques are being developed to address these two issues to provide reliable connectivity…
Low-density parity-check (LDPC) codes with the parity-based approach for distributed joint source channel coding (DJSCC) with decoder side information is described in this paper. The parity-based approach is theoretical limit achievable.…
Spatially coupled low-density parity-check codes show an outstanding performance under the low-complexity belief propagation (BP) decoding algorithm. They exhibit a peculiar convergence phenomenon above the BP threshold of the underlying…
This paper investigates decoder diversity architectures for short low-density parity-check (LDPC) codes, based on recurrent neural network (RNN) models of the belief-propagation (BP) algorithm. We propose a new approach to achieve decoder…
An efficient decoder is essential for quantum error correction, and data-driven neural decoders have emerged as promising, flexible solutions. Here, we introduce a diffusion model framework to infer logical errors from syndrome measurements…
We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in…
This paper describes an efficient implementation of binning for the relay channel using low-density parity-check (LDPC) codes. We devise bilayer LDPC codes to approach the theoretically promised rate of the decode-and-forward relaying…
This paper proposes two approaches for reducing the impact of the error floor phenomenon when decoding quantum low-density parity-check codes with belief propagation based algorithms. First, a low-complexity syndrome-based linear…