A note on classification of binary signal set in the view of Hadamard equivalence

Ki Hyeon Park, Hong Yeop Song

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

Abstract

In this paper, we derive a kind of classification of binary signal set by adopting Hadamard equivalence of binary matrices. We propose a fast algorithm for checking the Hadamard equivalence for general binary matrices, and give an intuitive analysis on its time complexity. For this, we define Hadamard-equivalence on the set of binary matrices, and a function which induces a total order on them. With respect to this order relation, we define the minimal element which is used as a representative of an equivalence class. We applied the proposed algorithm to binary matrices of smaller sizes, and show the results. Finally, we discuss a new combinatorial problem of counting the number of and enumerating all the inequivalent binary minimal matrices of size m x n, and show the solutions for small sizes, leaving many of the observed properties as open problems.

Original languageEnglish
Title of host publicationProceedings of the 4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09
Pages100-103
Number of pages4
DOIs
Publication statusPublished - 2009
Event4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09 - Fukuoka, Japan
Duration: 2009 Oct 192009 Oct 23

Publication series

NameProceedings of the 4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09

Other

Other4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09
CountryJapan
CityFukuoka
Period09/10/1909/10/23

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Signal Processing
  • Electrical and Electronic Engineering
  • Communication

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    Park, K. H., & Song, H. Y. (2009). A note on classification of binary signal set in the view of Hadamard equivalence. In Proceedings of the 4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09 (pp. 100-103). [5346402] (Proceedings of the 4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09). https://doi.org/10.1109/IWSDA.2009.5346402