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Detection of Skew in a Sequence of Subsets

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Abstract

Let C be a set whose elements are subsets of {1,2,..., n}. We call the set C a code and its elements codewords. Assume that we transmit a sequence c 1, c 2,...,c m,..., where each c i is a codeword in C with its elements in any order and the receiver receives a sequence c1, c2,..., cm,..., where each ci is equal to c i with perhaps some skew from the previous and following codewords. The idea is to decode correctly the codewords when there is no skew between consecutive codewords, and to detect the occurrence of skew below a certain threshold.

In this paper, we define the concept of skew and give necessary and sufficient conditions for codes detecting skew not exceeding a certain threshold. We present some code constructions and discuss their optimality. Finally, we mention possible applications for parallel asynchronous communications.

Keywords

  • Binary Vector
  • Cyclic Code
  • Decode Algorithm
  • Parity Check Matrix
  • Binary Linear Code

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1993 Springer-Verlag New York, Inc.

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Blaum, M., Bruck, J. (1993). Detection of Skew in a Sequence of Subsets. In: Capocelli, R., De Santis, A., Vaccaro, U. (eds) Sequences II. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9323-8_2

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  • DOI: https://doi.org/10.1007/978-1-4613-9323-8_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9325-2

  • Online ISBN: 978-1-4613-9323-8

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