Related papers: Relaxed Locally Correctable Codes in Computational…
In the two-part paper, we consider the problem of secure network coding when the information rate and the security level can change over time. To efficiently solve this problem, we put forward local-encoding-preserving secure network…
More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also…
We study a quantum analogue of locally decodable error-correcting codes. A q-query locally decodable quantum code encodes n classical bits in an m-qubit state, in such a way that each of the encoded bits can be recovered with high…
Linear error-correcting codes form the mathematical backbone of modern digital communication and storage systems, but identifying champion linear codes (linear codes achieving or exceeding the best known minimum Hamming distance) remains…
We consider an \textit{Adaptive Random Convolutional Network Coding} (ARCNC) algorithm to address the issue of field size in random network coding for multicast, and study its memory and decoding delay performances through both analysis and…
This paper investigates achievable information rates and error exponents of mismatched decoding when the channel belongs to the class of channels that are close to the decoding metric in terms of relative entropy. For both discrete- and…
We present a general framework for derandomizing random linear codes with respect to a broad class of properties, known as local properties, which encompass several standard notions such as distance, list-decoding, list-recovery, and…
Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to compute some global structural feature of the graph. Such algorithms use only local information available at nodes to determine local aspects of the…
Recently, a coding technique called position-based coding has been used to establish achievability statements for various kinds of classical communication protocols that use quantum channels. In the present paper, we apply this technique in…
Locally repairable codes (LRCs), which can recover any symbol of a codeword by reading only a small number of other symbols, have been widely used in real-world distributed storage systems, such as Microsoft Azure Storage and Ceph Storage…
This paper investigates data compression that simultaneously allows local decoding and local update. The main result is a universal compression scheme for memoryless sources with the following features. The rate can be made arbitrarily…
We investigate joint network and channel coding schemes for networks when relay nodes are not capable of performing channel coding operations. Rather, channel encoding is performed at the source node while channel decoding is done only at…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
Tamper-resilient cryptography studies how to protect data against adversaries who can physically manipulate codewords before they are decoded. The notion of tamper detection codes formalizes this goal, requiring that any unauthorized…
We present a general framework for constructing high rate error correcting codes that are locally correctable (and hence locally decodable if linear) with a sublinear number of queries, based on lifting codes with respect to functions on…
We study *non-adaptive* Local Computation Algorithms (LCA). A reduction of Parnas and Ron (TCS'07) turns any distributed algorithm into a non-adaptive LCA. Plugging known distributed algorithms, this leads to non-adaptive LCAs for constant…
Constructions of optimal locally repairable codes (LRCs) in the case of $(r+1) \nmid n$ and over small finite fields were stated as open problems for LRCs in [I. Tamo \emph{et al.}, "Optimal locally repairable codes and connections to…
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…
Locally recoverable codes deal with the task of reconstructing a lost symbol by relying on a portion of the remaining coordinates smaller than an information set. We consider the case of codes over finite chain rings, generalizing known…
A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…