Related papers: High Rate Efficient Local List Decoding from HDX
We improve the method in \cite{Seidl:10} for increasing the finite-lengh performance of polar codes by protecting specific, less reliable symbols with simple outer repetition codes. Decoding of the scheme integrates easily in the known…
We construct $3$-query relaxed locally decodable codes (RLDCs) with constant alphabet size and length $\tilde{O}(k^2)$ for $k$-bit messages. Combined with the lower bound of $\tilde{\Omega}(k^3)$ of [Alrabiah, Guruswami, Kothari, Manohar,…
We investigate the distance properties of linear locally recoverable codes (LRC codes) with all-symbol locality and availability. New upper and lower bounds on the minimum distance of such codes are derived. The upper bound is based on the…
We consider integer and linear programming problems for which the linear constraints exhibit a (recursive) block-structure: The problem decomposes into independent and efficiently solvable sub-problems if a small number of constraints is…
We present a new model for LT codes which simplifies the analysis of the error probability of decoding by belief propagation. For any given degree distribution, we provide the first rigorous expression for the limiting error probability as…
Due to the ability to provide superior error-correction performance, the successive cancellation list (SCL) algorithm is widely regarded as one of the most promising decoding algorithms for polar codes with short-to-moderate code lengths.…
We give a construction of Quantum Low-Density Parity Check (QLDPC) codes with near-optimal rate-distance tradeoff and efficient list decoding up to the Johnson bound in polynomial time. Previous constructions of list decodable good distance…
Distributed computation is a framework used to break down a complex computational task into smaller tasks and distributing them among computational nodes. Erasure correction codes have recently been introduced and have become a popular…
We consider a class of popular distributed non-convex optimization problems, in which agents connected by a network $\mathcal{G}$ collectively optimize a sum of smooth (possibly non-convex) local objective functions. We address the…
Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems. In an LRC code, any erased symbol of a codeword can be recovered…
We consider error decoding of locally repairable codes (LRC) and partial MDS (PMDS) codes through interleaved decoding. For a specific class of LRCs we investigate the success probability of interleaved decoding. For PMDS codes we show that…
We extend the notion of locality from the Hamming metric to the rank and subspace metrics. Our main contribution is to construct a class of array codes with locality constraints in the rank metric. Our motivation for constructing such codes…
We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability and for the remaining queries, the decoder…
Hyperdimensional Computing (HDC) is an emerging computational paradigm for representing compositional information as high-dimensional vectors, and has a promising potential in applications ranging from machine learning to neuromorphic…
The minimum distance is one of the most important combinatorial characterizations of a code. The maximum likelihood decoding problem is one of the most important algorithmic problems of a code. While these problems are known to be hard for…
Quantum low-density parity-check (qLDPC) codes are an important component in the quest for quantum fault tolerance. Dramatic recent progress on qLDPC codes has led to constructions which are asymptotically good, and which admit linear-time…
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 $t$…
Regenerating codes and codes with locality are two schemes that have recently been proposed to ensure data collection and reliability in a distributed storage network. In a situation where one is attempting to repair a failed node,…
In this paper, we investigate a coupled polar code architecture that supports both local and global decoding. This local-global construction is motivated by practical applications in data storage and transmission where reduced-latency…
Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and…