Kasami sequences, named after Japanese information theorist Tadao Kasami, are binary sequences of length 2N−1 where N is an even integer.1 Kasami sequences have good cross-correlation values approaching the Welch lower bound. They are used as low-correlation spreading sequences in spread-spectrum communication systems.2 There are two classes of Kasami sequences—the small set and the large set.
Kasami Set
The process of generating a Kasami sequence is initiated by generating a maximum length sequence a(n), where n = 1…2N−1. Maximum length sequences are periodic sequences with a period of exactly 2N−1. Next, a secondary sequence is derived from the initial sequence via cyclic decimation sampling as b(n) = a(q ⋅ n), where q = 2N/2+1. Modified sequences are then formed by adding a(n) and cyclically time shifted versions of b(n) using modulo-two arithmetic, which is also termed the exclusive or (xor) operation. Computing modified sequences from all 2N/2 unique time shifts of b(n) forms the Kasami set of code sequences.
References
References
- Kasami, Tadao; Kohno, Ryuji (2002). "Kasami Sequences". Encyclopedia of Telecommunications. John Wiley & Sons.
- Goiser, Alois M. J. (1998). "4.4 Kasami-Folgen" [Kasami sequences]. Handbuch der Spread-Spectrum Technik [Handbook of the spread-spectrum technique] (in German) (1 ed.). Vienna, Austria: Springer Verlag. ISBN 3-211-83080-4.
- Kasami, Tadao (1966). Weight Distribution Formula for Some Class of Cyclic Codes (PDF) (Technical report). University of Illinois. hdl:2142/74439. R285.
- Welch, Lloyd Richard (May 1974). "Lower Bounds on the Maximum Cross Correlation of Signals". IEEE Transactions on Information Theory. 20 (3): 397–399. doi:10.1109/TIT.1974.1055219.
- Goiser, Alois M. J. (1998). "4.4 Kasami-Folgen" [Kasami sequences]. Handbuch der Spread-Spectrum Technik [Handbook of the spread-spectrum technique] (in German) (1 ed.). Vienna, Austria: Springer Verlag. ISBN 3-211-83080-4.