Related papers: Performance Analysis based on Density Evolution on…
A low-density parity-check (LDPC) code is a linear block code described by a sparse parity-check matrix, which can be efficiently represented by a bipartite Tanner graph. The standard iterative decoding algorithm, known as belief…
Tensor network contraction on arbitrary graphs is a fundamental computational challenge with applications ranging from quantum simulation to error correction. While belief propagation (BP) provides a powerful approximation algorithm for…
Hypergraph product codes are a class of constant-rate quantum low-density parity-check (LDPC) codes equipped with a linear-time decoder called small-set-flip (SSF). This decoder displays sub-optimal performance in practice and requires very…
Iterative probabilistic inference, popularly dubbed the soft-iterative paradigm, has found great use in a wide range of communication applications, including turbo decoding and turbo equalization. The classic approach of analyzing the…
This paper considers the performance of $(j,k)$-regular low-density parity-check (LDPC) codes with message-passing (MP) decoding algorithms in the high-rate regime. In particular, we derive the high-rate scaling law for MP decoding of LDPC…
Belief propagation (BP) is a powerful tool to solve distributed inference problems, though it is limited by short cycles in the corresponding factor graph. Such cycles may lead to incorrect solutions or oscillatory behavior. Only for…
We design iterative receiver schemes for a generic wireless communication system by treating channel estimation and information decoding as an inference problem in graphical models. We introduce a recently proposed inference framework that…
Permutation decoding gained recent interest as it can exploit the symmetries of a code in a parallel fashion. Moreover, it has been shown that by viewing permuted polar codes as polar subcodes, the set of usable permutations in permutation…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
The design of codes for feedback-enabled communications has been a long-standing open problem. Recent research on non-linear, deep learning-based coding schemes have demonstrated significant improvements in communication reliability over…
In this paper, we consider quantized decoding of LDPC codes on the binary symmetric channel. The binary message passing algorithms, while allowing extremely fast hardware implementation, are not very attractive from the perspective of…
Belief propagation (BP) algorithm is a widely used message-passing method for inference in graphical models. BP on loop-free graphs converges in linear time. But for graphs with loops, BP's performance is uncertain, and the understanding of…
Decoding Bivariate Bicycle (BB) quantum error correction codes typically requires Belief Propagation (BP) followed by Ordered Statistics Decoding (OSD) post-processing when BP fails to converge. Whether BP will converge on a given syndrome…
Paper [1] derived the probability density function (PDF) of a sum of products of two correlated complex Gaussian zero-mean random variables (RVs) that has been applied to calculate the error probabilities of a \emph{M}-ary phase shift…
Message-passing iterative decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudo-codewords. These failures can cause the large signal-to-noise ratio performance of…
Finite alphabet iterative decoders (FAID) with multilevel messages that can surpass BP in the error floor region for LDPC codes on the BSC were previously proposed. In this paper, we propose decimation-enhanced decoders. The technique of…
Numerical issues related to the occurrence of error floors in floating-point simulations of belief propagation (BP) decoders are examined. Careful processing of messages corresponding to highly-certain bit values can sometimes reduce error…
Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and…
Fault-tolerant quantum computers will depend crucially on the performance of the classical decoding algorithm which takes in the results of measurements and outputs corrections to the errors inferred to have occurred. Machine learning…
Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces…