On the capacity of precision-resolution constrained systems

Moshe Schwartz, Jehoshua Bruck

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

Abstract

Arguably, the most famous constrained system is the (d,k)-RLL (Run-Length Limited), in which a stream of bits obeys the constraint that every two l's are separated by at least d O's, and there are no more than k consecutive O's anywhere in the stream. The motivation for this scheme comes from the fact that certain sensor characteristics restrict the minimum time between adjacent l's or else the two will be merged in the receiver, while a clock drift between transmitter and receiver may cause spurious O's or missing O's at the receiver if too many appear consecutively. The interval-modulation scheme introduced by Mukhtar and Bruck extends the RLL constraint and implicitly suggests a way of taking advantage of higher-precision clocks. Their work however, deals only with an encoder/decoder construction. In this work we introduce a more general framework which we call the precision-resolution (PR) constrained system. In PR systems, the encoder has precision constraints, while the decoder has resolution constraints. We examine the capacity of PR systems and show the gain in the presence of a high-precision encoder (thus, we place the PR system with integral encoder, (p=1, α, θ)-PR, which turns out to be a simple extension of RLL, and the PR system with infinite-precision encoder, (∞, α, θ)-PR, on two ends of a continuum). We derive an exact expression for their capacity in terms of the precision p, the minimal resolvable measurement at the decoder α, and the decoder resolution factor θ. In an analogy to the RLL terminology these are the clock precision, the minimal time between peaks, and the clock drift. Surprisingly, even with an infinite-precision encoder, the capacity is finite.

Original languageEnglish
Title of host publicationProceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006
Pages1462-1466
Number of pages5
DOIs
StatePublished - 1 Dec 2006
Externally publishedYes
Event2006 IEEE International Symposium on Information Theory, ISIT 2006 - Seattle, WA, United States
Duration: 9 Jul 200614 Jul 2006

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8101

Conference

Conference2006 IEEE International Symposium on Information Theory, ISIT 2006
Country/TerritoryUnited States
CitySeattle, WA
Period9/07/0614/07/06

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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