Topics in Pseudonoise Sequence Design and Error-Correcting Codes

University Of Southern California, Los Angeles CA

Investigators

Abstract

In this project, algebraic techniques are in use two to tackle two classes of problems related to improving the throughput and/or reliability of a communication link are under study. The first class of problems under study is the design of long and efficient error-correcting codes. Such codes are of interest as longer error-correcting codes tend to ``average'' out the noise and hence provide better performance. The second class of problems relates to the design and analysis of families of signature sequences that are used to distinguish between the signals of different users in a multi-user environment. Examples of multi-user environments include Code Division Multiple Access (CDMA) cellular and personal communication systems. More details on example problems drawn from each class are provided below. Since the early 80's, the promise of algebraic geometric (AG) codes has been the delivery of a sequence of error-correcting codes of increasing length whose asymptotic performance exceeds the Gilbert-Varshamov bound and for which efficient and practical encoding and decoding algorithms are available. Computationally efficient decoding algorithms for AG codes are now available and there now exist explicit descriptions of algebraic curves of the type required to construct these long codes. Construction of good codes on these curves requires the determination of a basis for a certain type of vector space of functions defined on these curves. The investigators study efficient methods of generating such bases. The use of novel algebraic geometry techniques to generate pseudo-random sequences is an example of the type of problem belonging to the second class. The investigators examine methods of generating sequences having pseudo-random properties such as low correlation and large linear span. Also under investigation are more efficient means of assessing the performance of pseudo-random sequences in a multi-user setting, for example, more efficient means of determining the minimum Euclidean distance between adjacent multi-user signals. The performance in a multi-user setting, of a a specific sequence family, known as family S(2) and previously co-designed by the PI is also under study.