Error Detection and Correction in Communication Networks

Chong Shangguan, Itzhak Tamo

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Let G be a connected graph on n vertices and C be an (n,k,d) code with d ≥ 2, defined on the alphabet {0,1}m. Suppose that for 1 ≤ i ≤ n, the i-th vertex of G holds an input symbol xi {0,1}m and let x = (x1,⋯,xn) {0,1}mn be the input vector formed by those symbols. Assume that each vertex of G can communicate with its neighbors by transmitting messages along the edges, and these vertices must decide deterministically, according to a predetermined communication protocol, that whether x C. Then what is the minimum communication cost to solve this problem? Moreover, if x C, say, there is less than \lfloor {(d - 1}\right)/2} \right\rfloor input errors among the xi's, then what is the minimum communication cost for error correction?We initiate the study of the two problems mentioned above. For the error detection problem, we obtain two lower bounds on the communication cost as functions of n,k,d,m, and our bounds are tight for several graphs and codes. For the error correction problem, we design a protocol which can efficiently correct a single input error when G is a cycle and C is a repetition code.

Original languageEnglish
Title of host publication2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages96-101
Number of pages6
ISBN (Electronic)9781728164328
DOIs
StatePublished - Jun 2020
Event2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States
Duration: 21 Jul 202026 Jul 2020

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2020-June
ISSN (Print)2157-8095

Conference

Conference2020 IEEE International Symposium on Information Theory, ISIT 2020
Country/TerritoryUnited States
CityLos Angeles
Period21/07/2026/07/20

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