Shift-invariant protocol sequences for the collision channel without feedback

  • Authors:
  • Kenneth W. Shum;Chung Shue Chen;Chi Wan Sung;Wing Shing Wong

  • Affiliations:
  • Department of Information Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong;PNA2 Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands and Department of Electronics and Telecommunications, Norwegian University of Science and Technology, Norway;Department of Electronic Engineering, City University of Hong Kong, Kowloon Tong, Hong Kong;Department of Information Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2009

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Abstract

We consider collision channel without feedback in which collided packets are considered unrecoverable. For each user, the transmission of packets follows a specific periodical pattern, called the protocol sequence. Due to the lack of feedback, the beginning of the protocol sequences cannot be synchronized and nonzero relative offsets are inevitable. It results in variation of throughput. In this paper, we investigate optimal protocol sequence sets, in the sense that the throughput variance is zero. Such protocol sequences are said to be shift-invariant (SI). The characterizing properties of SI protocol sequences are presented. We also prove that SI sequences are identifiable, meaning that the receiver is able to determine the sender of each successfully received packet without any packet header. A general construction of SI sequences that meets the lower bound on sequence length is given. Besides, we study the least periods of SI sequences, and show that the least periods must be distinct in some cases. The throughput performance is compared numerically with other protocol sequences.