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This thesis makes several significant contributions to the theory of both Regenerating (RG) and Locally Recoverable (LR) codes. The two principal contributions are characterizing the optimal rate of an LR code designed to recover from $t$…
Patients with motor control difficulties often "type" on a computer using a switch keyboard to guide a scanning cursor to text elements. We show how to optimize some parts of the design of switch keyboards by casting the design problem as…
We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every $0 < R < 1$ and $\eps> 0$, we present an explicit construction of…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem which is gaining relevance thanks to emerging applications in wireless communication networks. In this work, we…
The iteration complexity of the block-coordinate descent (BCD) type algorithm has been under extensive investigation. It was recently shown that for convex problems the classical cyclic BCGD (block coordinate gradient descent) achieves an…
In this paper, we consider the problem of constructing optimal average-length binary codes under the constraint that each codeword must contain at most $D$ ones, where $D$ is a given input parameter. We provide an $O(n^2D)$-time complexity…
This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
Redistricting practitioners must balance many competing constraints and criteria when drawing district boundaries. To aid in this process, researchers have developed many methods for optimizing districting plans according to one or more…
We give new sublinear and parallel algorithms for the extensively studied problem of approximating n-variable r-CSPs (constraint satisfaction problems with constraints of arity r up to an additive error. The running time of our algorithms…
Error-correcting codes over the real field are studied which can locate outlying computational errors when performing approximate computing of real vector--matrix multiplication on resistive crossbars. Prior work has concentrated on…
Gradient coding is a technique for straggler mitigation in distributed learning. In this paper we design novel gradient codes using tools from classical coding theory, namely, cyclic MDS codes, which compare favorably with existing…
Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems…
Max Restricted Path Consistency (maxRPC) is a local consistency for binary constraints that can achieve considerably stronger pruning than arc consistency. However, existing maxRRC algorithms suffer from overheads and redundancies as they…
We give new constructions of two classes of algebraic code families which are efficiently list decodable with small output list size from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired…
We present a novel iterative decoding algorithm for Reed-Muller (RM) codes, which takes advantage of a graph representation of the code. Vertices of the considered graph correspond to codewords, with two vertices being connected by an edge…
It is shown that some well-known and some new cyclic codes with orthogonal parity-check equations can be constructed in the finite-field transform domain. It is also shown that, for some binary linear cyclic codes, the performance of the…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…
This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…
Ongoing research and experiments have enabled quantum memory to realize the storage of qubits. On the other hand, interleaving techniques are used to deal with burst of errors. Effective interleaving techniques for combating burst of errors…