Design of Kronecker and Combination Sequences and Comparison of Their Correlation, CDMA and Information Security Properties

Kari H. A. KARKKAINEN  Pentti A. LEPPANEN  

Publication
IEICE TRANSACTIONS on Communications   Vol.E81-B   No.9   pp.1770-1778
Publication Date: 1998/09/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Mobile Communication
Keyword: 
spreading codes,  rapid code synchronization,  code-division multiple-access,  correlation,  linear complexity,  

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Summary: 
Two families of rapidly synchronizable spreading codes are compared using the same component codes. The influence of component code choice is also discussed. It is concluded that correlation, code-division multiple-access (CDMA) and information security (measured by the value of linear complexity) properties of Kronecker sequences are considerably better than those of Combination sequences. Combination sequences cannot be recommended for CDMA use unless the number of active users is few. CDMA performance of Kronecker sequences is almost comparable with that of linear pseudonoise (PN) code families of equal length when a Gold or Kasami code is used as the innermost code and the Barker code is used as the outermost code to guarantee satisfactory correlation and CDMA properties. Kronecker sequences possess a considerably higher value of linear complexity than those of the corresponding non-linear Geffe and majority logic type combination sequences. This implies they are highly non-linear codes due to the Kronecker product construction method. It is also observed that the Geffe type Boolean combiner resulted in better correlation and CDMA performance than with majority logic. The use of the purely linear exclusive-or combiner for considerable reduction of code synchronization time is not found recommendable although it results in good CDMA performance.