A Survey of the Linear Complexity of Binary Sequences with Optimal Autocorrelation

PhD Qualifying Examination


Title: "A Survey of the Linear Complexity of Binary Sequences with Optimal
Autocorrelation"

Mr. Qi WANG


Abstract:

Sequences have important applications in ranging systems, spread spectrum 
communication systems, code division multiple access (CDMA) communication 
systems, global positioning systems (GPS), and stream ciphers etc. 
Sequences having desirable properties are strongly needed in these 
applications, of which randomness and complexity are the most important 
two. Randomness refers to the unpredictability of the sequence, while 
complexity describes the difficulty of replicating the sequence. In this 
paper, we concentrate on two main properties of binary sequences. One is 
the autocorrelation, which describes the randomness of the sequence, and 
the other is linear complexity which is the most popular measure for 
complexity. To characterize binary sequences with optimal autocorrelation, 
we introduce the corresponding two combinatorial characterizations, say, 
difference sets and almost difference sets. We also give a well rounded 
treatment of binary sequences with optimal autocorrelation, survey the 
current known constructions for binary sequences with optimal 
autocorrelation, and discuss the linear complexities of these binary 
sequences. Based on the known constructions, we summarize the methods of 
computing the linear complexity of sequences.


Date:     		Wednesday, 11 February 2009

Time:                   10:30a.m.-12:30p.m.

Venue:                  Room 4483
 			lifts 25-26

Committee Members:      Prof. Cunsheng Ding (Supervisor)
 			Dr. Huamin Qu (Chairperson)
 			Dr. Ke Yi
 			Dr. Wai-Ho Mow (ECE)
 			Dr. M. Z. Wang (Elec. & Inf. Engg., PolyU.)


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