相关论文: Multilevel expander codes

A $z$-matching on a bipartite graph is a set of edges, among which each vertex of two types of the graph is adjacent to at most $1$ and at most $z$ ($\geqslant 1$) edges, respectively. The $z$-matching problem concerns finding $z$-matchings…

This paper investigates a unification of distributed source coding, multiple description coding, and source coding with side information at decoders. The equivalence between the multiple-decoder extension of distributed source coding with…

We consider upper bounds on the error probability in channel coding. We derive an improved maximum-likelihood union bound, which takes into account events where the likelihood of the correct codeword is tied with that of some competitors.…

We provide a multilevel approach for analysing performances of parallel algorithms. The main outcome of such approach is that the algorithm is described by using a set of operators which are related to each other according to the problem…

We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…

Graph code is a linear code obtained from linear codes $C$ and a certain bipartite graph G. In this paper, I propose an expansion of the definition of graph code to general $l$-partite, and give its lower bound of minimum distance. I also…

We consider the decoding of LDPC codes over GF(q) with the low-complexity majority algorithm from [1]. A modification of this algorithm with multiple thresholds is suggested. A lower estimate on the decoding radius realized by the new…

This paper considers the optimization of multi-edge type low-density parity-check (METLDPC) codes to maximize the decoding threshold. We propose an algorithm to jointly optimize the node degree distribution and the multi-edge structure of…

In this paper, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbol-pair read channel has recently been introduced by Cassuto and Blaum to model channels with high write resolution but low read…

Multilayer networks preserve full information about the different interactions among the constituents of a complex system, and have recently proven quite useful in modelling transportation networks, social circles, and the human brain. A…

A rate-dependent upper bound of the best achievable block error probability of polar codes with successive-cancellation decoding is derived.

For finite sequence $\underbar{\em d}$ of positive integers, we consider graphs that have $\underbar{\em d}$ as their list of vertex degrees, and bipartite graphs for which each part has $\underbar{\em d}$ as its list of vertex degrees. In…

We construct constant-sized ensembles of linear error-correcting codes over any fixed alphabet that can correct a given fraction of adversarial erasures at rates approaching the Singleton bound arbitrarily closely. We provide several…

Lifted Reed-Solomon codes and multiplicity codes are two classes of evaluation codes that allow for the design of high-rate codes that can recover every codeword or information symbol from many disjoint sets. Recently, the underlying…

Bilevel programming problems frequently arise in real-world applications across various fields, including transportation, economics, energy markets and healthcare. These problems have been proven to be NP-hard even in the simplest form with…

Bilevel optimization has gained significant attention in recent years due to its broad applications in machine learning. This paper focuses on bilevel optimization in decentralized networks and proposes a novel single-loop algorithm for…

This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error…

This paper studies channel coding for the discrete memoryless multiple-access channel with a given (possibly suboptimal) decoding rule. A multi-letter successive decoding rule depending on an arbitrary non-negative decoding metric is…

We consider the algorithmic complexity of recognizing bipartite temporal graphs. Rather than defining these graphs solely by their underlying graph or individual layers, we define a bipartite temporal graph as one in which every layer can…

We extend the concept of graph isomorphisms to multilayer networks with any number of "aspects" (i.e., types of layering). In developing this generalization, we identify multiple types of isomorphisms. For example, in multilayer networks…