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In this paper we propose a novel parallel stochastic coordinate descent (SCD) algorithm with convergence guarantees that exhibits strong scalability. We start by studying a state-of-the-art parallel implementation of SCD and identify…

We present a tree-based construction of LDPC codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a $d$-regular tree…

We propose a novel encoding/transmission scheme called continuous chain (CC) transmission that is able to improve the finite-length performance of a system using spatially-coupled low-density parity-check (SC-LDPC) codes. In CC…

We consider distributed gradient descent in the presence of stragglers. Recent work on \em gradient coding \em and \em approximate gradient coding \em have shown how to add redundancy in distributed gradient descent to guarantee convergence…

We study a class of linear network coding (LNC) schemes, called circular-shift LNC, whose encoding operations consist of only circular-shifts and bit-wise additions (XOR). Formulated as a special vector linear code over GF($2$), an…

Linear constrained switching systems are linear switched systems whose switching sequences are constrained by a deterministic finite automaton. This work investigates how to generate a sequence of matrices with an asymptotic growth rate…

In this paper, we leverage polar codes and the well-established channel polarization to design capacity-achieving codes with a certain constraint on the weights of all the columns in the generator matrix (GM) while having a low-complexity…

Constructions of locally decodable codes (LDCs) have one of two undesirable properties: low rate or high locality (polynomial in the length of the message). In settings where the encoder/decoder have already exchanged cryptographic keys and…

This paper investigates the design of self-connected spatially coupled low-density parity-check (SC-LDPC) codes. First, a termination method is proposed to reduce rate loss. Particularly, a single-side open SC-LDPC ensemble is introduced,…

In this paper, we propose a new coded computing technique called "substitute decoding" for general iterative distributed computation tasks. In the first part of the paper, we use PageRank as a simple example to show that substitute decoding…

The performance and the decoding complexity of a novel coding scheme based on the concatenation of maximum distance separable (MDS) codes and linear random fountain codes are investigated. Differently from Raptor codes (which are based on a…

We consider the problem of coded computing, where a computational task is performed in a distributed fashion in the presence of adversarial workers. We propose techniques to break the adversarial toleration threshold barrier previously…

Cyclic liftings are proposed to lower the error floor of low-density parity-check (LDPC) codes. The liftings are designed to eliminate dominant trapping sets of the base code by removing the short cycles which form the trapping sets. We…

It was recently shown that spatial coupling of individual low-density parity-check codes improves the belief-propagation threshold of the coupled ensemble essentially to the maximum a posteriori threshold of the underlying ensemble. We…

Spatially-coupled low-density parity-check (LDPC) codes, which were first introduced as LDPC convolutional codes, have been shown to exhibit excellent performance under low-complexity belief-propagation decoding. This phenomenon is now…

Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to speed up matrix problems including matrix completion, subspace tracking, and SDP relaxation. In this paper, we exhibit a step size scheme for SGD on a…

Designing good error correcting codes whose generator matrix has a support constraint, i.e., one for which only certain entries of the generator matrix are allowed to be non-zero, has found many recent applications, including in distributed…

We consider the problem of evaluating arbitrary multivariate polynomials over a massive dataset containing multiple inputs, on a distributed computing system with a master node and multiple worker nodes. Generalized Lagrange Coded Computing…

This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in…

We present a general approach to designing capacity-approaching high-girth low-density parity-check (LDPC) codes that are friendly to hardware implementation. Our methodology starts by defining a new class of "hierarchical" quasi-cyclic…