Related papers: The Sum-Product Algorithm for Degree-2 Check Nodes…
While feasibility and obtaining a solution of a given network coding problem are well studied, the decoding procedure and complexity have not garnered much attention. We consider the decoding problem in a network wherein the sources…
A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…
Low-density parity-check codes, a class of capacity-approaching linear codes, are particularly recognized for their efficient decoding scheme. The decoding scheme, known as the sum-product, is an iterative algorithm consisting of passing…
While the capacity, feasibility and methods to obtain codes for network coding problems are well studied, the decoding procedure and complexity have not garnered much attention. In this work, we pose the decoding problem at a sink node in a…
We consider linear-programming (LP) decoding of low-density parity-check (LDPC) codes. While it is clear that one can use any general-purpose LP solver to solve the LP that appears in the decoding problem, we argue in this paper that the LP…
A sum-product network (SPN) is a probabilistic model, based on a rooted acyclic directed graph, in which terminal nodes represent univariate probability distributions and non-terminal nodes represent convex combinations (weighted sums) and…
Two-level logic minimization is a central problem in logic synthesis, and has applications in reliability analysis and automated reasoning. This paper represents a method of minimizing Boolean sum of products function with binary decision…
A constant-rate encoder--decoder pair is presented for a fairly large family of two-dimensional (2-D) constraints. Encoding and decoding is done in a row-by-row manner, and is sliding-block decodable. Essentially, the 2-D constraint is…
Many datasets take the form of a bipartite graph where two types of nodes are connected by relationships, like the movies watched by a user or the tags associated with a file. The partitioning of the bipartite graph could be used to fasten…
Sum-rank-metric codes have wide applications in the multishot network coding and the distributed storage. Linearized Reed-Solomon codes, sum-rank BCH codes and their Welch-Berlekamp type decoding algorithms were proposed and studied. They…
Cooperative optimization is a new way for finding global optima of complicated functions of many variables. It has some important properties not possessed by any conventional optimization methods. It has been successfully applied in solving…
In this paper, we show how to construct a factor graph from a network code. This provides a systematic framework for decoding using message passing algorithms. The proposed message passing decoder exploits knowledge of the underlying…
This paper introduces a deterministic algorithm for solving an instance of the Subset Sum Problem based on a new method entitled the Bipartite Synthesis Method. The algorithm is described and shown to have worst-case limiting performance…
Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…
We study the sum-product problem for the planar hypercomplex numbers: the dual numbers and double numbers. These number systems are similar to the complex numbers, but it turns out that they have a very different combinatorial behavior. We…
An efficient algorithm for classification of binary self-dual codes is presented. As an application, a complete classification of the self-dual codes of length 38 is given.
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
We address an open problem posed by Chen-Cheng-Qi (IEEE Trans.\ Inf.\ Theory, 2025): can the decoding of binary sum-rank-metric codes $\SR(C_1,C_2)$ with $2\times2$ matrix blocks be reduced entirely to decoding the constituent…
The tree-depth problem can be seen as finding an elimination tree of minimum height for a given input graph $G$. We introduce a bicriteria generalization in which additionally the width of the elimination tree needs to be bounded by some…
We propose a recursive algorithm for identifying all finite sequences of positive integers whose product equals their sum. Our method uses solutions of strictly shorter length that are iteratively extended in pursuit of a valid solution.…