相关论文: Near Perfect Decoding of LDPC Codes

This paper is concerned with linear superposition systems in which all components of the superimposed signal are coded with an identical binary low-density parity-check (LDPC) code.

Product codes (PCs) and staircase codes (SCCs) are conventionally decoded based on bounded distance decoding (BDD) of the component codes and iterating between row and column decoders. The performance of iterative BDD (iBDD) can be improved…

In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…

In this paper, we investigate a class of submodular problems which in general are very hard. These include minimizing a submodular cost function under combinatorial constraints, which include cuts, matchings, paths, etc., optimizing a…

We study Low-Density Parity-Check (LDPC) codes with iterative decoding on block-fading (BF) Relay Channels. We consider two users that employ coded cooperation, a variant of decode-and-forward with a smaller outage probability than the…

This paper presents a theoretical study of a new type of LDPC codes motivated by practical storage applications. LDPCL codes (suffix L represents locality) are LDPC codes that can be decoded either as usual over the full code block, or…

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…

The design of optimal linear block codes capable of being efficiently decoded is of major concern, especially for short block lengths. As near capacity-approaching codes, Low-Density Parity-Check (LDPC) codes possess several advantages over…

In dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main…

Combinatorial optimization problems pose significant computational challenges across various fields, from logistics to cryptography. Traditional computational methods often struggle with their exponential complexity, motivating exploration…

Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…

We present a novel optimization-based decoding algorithm for LDPC codes that is suitable for hardware architectures specialized to feed-forward neural networks. The algorithm is based on the projected gradient descent algorithm with a…

We show that polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Reed-Solomon codes and, hence, can be collaboratively decoded. We consider a fault tolerant setup where $t$ worker nodes…

In this article the most fundamental decomposition-based optimization method - block coordinate search, based on the sequential decomposition of problems in subproblems - and building performance simulation programs are used to reason about…

The digital transformation of automation places new demands on data acquisition and processing in industrial processes. Logical relationships between acquired data and cyclic process sequences must be correctly interpreted and evaluated. To…

We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…

The paper is focused on the tradeoff between performance and decoding complexity per iteration for LDPC codes in terms of their gap (in rate) to capacity. The study of this tradeoff is done via information-theoretic bounds which also enable…

The error floor phenomenon, associated with iterative decoders, is one of the most significant limitations to the applications of low-density parity-check (LDPC) codes. A variety of techniques from code design to decoder implementation have…

Polar codes are a recently proposed family of provably capacity-achieving error-correction codes that received a lot of attention. While their theoretical properties render them interesting, their practicality compared to other types of…

Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…