### 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 language | English |
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Title of host publication | 2012 1st International Conference on Recent Advances in Information Technology, RAIT-2012 |

Pages | 177-181 |

Number of pages | 5 |

DOIs | |

Publication status | Published - 24 May 2012 |

Externally published | Yes |

Event | 2012 1st International Conference on Recent Advances in Information Technology, RAIT-2012 - Dhanbad, India Duration: 15 Mar 2012 → 17 Mar 2012 |

### Other

Other | 2012 1st International Conference on Recent Advances in Information Technology, RAIT-2012 |
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Country | India |

City | Dhanbad |

Period | 15/3/12 → 17/3/12 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Information Systems

### Cite this

*2012 1st International Conference on Recent Advances in Information Technology, RAIT-2012*(pp. 177-181). [6194501] https://doi.org/10.1109/RAIT.2012.6194501

**Energy-efficient communication : Understanding the distribution of runs in binary strings.** / Sinha, Koushik; Sinha, Bhabani P.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2012 1st International Conference on Recent Advances in Information Technology, RAIT-2012.*, 6194501, pp. 177-181, 2012 1st International Conference on Recent Advances in Information Technology, RAIT-2012, Dhanbad, India, 15/3/12. https://doi.org/10.1109/RAIT.2012.6194501

}

TY - GEN

T1 - Energy-efficient communication

T2 - Understanding the distribution of runs in binary strings

AU - Sinha, Koushik

AU - Sinha, Bhabani P.

PY - 2012/5/24

Y1 - 2012/5/24

N2 - 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.

AB - 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.

KW - Bernoulli's trial

KW - combinatorial problems

KW - energy-efficient communication

KW - run distribution

KW - run statistics

KW - Wireless sensor networks

UR - http://www.scopus.com/inward/record.url?scp=84862089685&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862089685&partnerID=8YFLogxK

U2 - 10.1109/RAIT.2012.6194501

DO - 10.1109/RAIT.2012.6194501

M3 - Conference contribution

AN - SCOPUS:84862089685

SN - 9781457706974

SP - 177

EP - 181

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

ER -