Energy-efficient communication: Understanding the distribution of runs in binary strings

Koushik Sinha, Bhabani P. Sinha

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

With the increasing use of wireless sensor networks (WSNs) in diverse applications where data to be communicated can range from few bytes of raw data to multimedia, the need for designing energy-efficient communication has attained paramount importance to increase the operational lifetime of such WSNs. Related to this issue, it is essential to understand the distribution of runs of 1's and 0's in the data to be transmitted, so that suitable communication techniques can be designed. Such a knowledge would also help in analyzing and comparing the performances of different energy-efficient communication techniques for a specific WSN application. In this paper, we derive a recurrence relation for expressing N k, the total number of occurrences of runs of 1's of length k, 1≤k≤n, in all possible binary strings of length n. Due to symmetry, N k is also the total number of occurrences of runs of 0's of length k, 1≤k≤n. We show that N n = 1, N n-1 = 2 and N n-k = (k + 3)2 k-2, for k≥2.

Original languageEnglish
Title of host publication2012 1st International Conference on Recent Advances in Information Technology, RAIT-2012
Pages177-181
Number of pages5
DOIs
Publication statusPublished - 24 May 2012
Event2012 1st International Conference on Recent Advances in Information Technology, RAIT-2012 - Dhanbad, India
Duration: 15 Mar 201217 Mar 2012

Publication series

Name2012 1st International Conference on Recent Advances in Information Technology, RAIT-2012

Other

Other2012 1st International Conference on Recent Advances in Information Technology, RAIT-2012
CountryIndia
CityDhanbad
Period15/3/1217/3/12

Keywords

  • Bernoulli's trial
  • Wireless sensor networks
  • combinatorial problems
  • energy-efficient communication
  • run distribution
  • run statistics

ASJC Scopus subject areas

  • Information Systems

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  • Cite this

    Sinha, K., & Sinha, B. P. (2012). Energy-efficient communication: Understanding the distribution of runs in binary strings. In 2012 1st International Conference on Recent Advances in Information Technology, RAIT-2012 (pp. 177-181). [6194501] (2012 1st International Conference on Recent Advances in Information Technology, RAIT-2012). https://doi.org/10.1109/RAIT.2012.6194501