Code design and analysis for multiple access communications
This thesis explores various coding aspects of multiple access communications, mainly for spread spectrum multiaccess(SSMA) communications and collaborative coding multiaccess(CCMA) communications. Both the SSMA and CCMA techniques permit efficient simultaneous transmission by several users sharing a common channel, without subdivision in time or frequency. The general principle behind these two multiaccess schemes is that one can find sets of signals (codes) which can be combined together to form a composite signal; on reception, the individual signals in the set can each be recovered from the composite signal. For the CCMA scheme, the isolation between users is based on the code structure; for the SSMA scheme, on the other hand, the isolation between users is based on the autocorrelation functions(ACFs) and crosscorrelation functions (CCFs) of the code sequences. It is clear that, in either case, the code design is the key to the system design. For the CCMA system with a multiaccess binary adder channel, a class of superimposed codes is analyzed. It is proved that every constant weight code of weight w and maximal correlation λ corresponds to a subclass of disjunctive codes of order T < w/λ. Results related to the decomposition of the disjunctive codes in the noiseless and noisy cases are derived. Decoding algorithms for both the noiseless and the noisy cases are proposed. For the CCMA system operating over a multiaccess Q-ary adder channel, a class of cyclic uniquely decodable codes is proposed and analyzed by employing cyclic codes with symbols from an arbitrary finite integer rings. A very low complexity decoding procedure is presented. For a synchronous SSMA system, a new approach employing orthogonal complementary sets is presented; the properties of such orthogonal complementary sets are studied in detail. Recursive formulas for constructing orthogonal complementary sets are given. Methods for synthesizing new orthogonal complementary sets from known ones with the same dimensions are also discussed. For an asynchronous SSMA system, several new spreading codes are presented and studied: 1. A new class of polyphase codes with two-valued periodic ACF and CCF properties is derived. It is proved that, for a given prime length L > 3, the out-of-phase ACFs and CCFs of the codes are constant and equal to √L. In addition, all codes of the same length are mutually orthogonal. 2. Maximal length sequences (m-sequences) over Gaussian integers, suitable for use with QAM modulation, are considered. Two sub-classes of m-sequences with quasi-perfect periodic autocorrelations are obtained. The CCFs between the decimated m-sequences are studied. By applying a simple operation, it is shown that some m-sequences over rational and Gaussian integers can be transformed into perfect sequences with impulsive ACFs. 3. Frank codes and Chu codes have perfect periodic ACFs and optimum periodic CCFs. In addition, it is shown that they also have very favourable nonperiodic ACFs; some new results concerning the behaviour of the nonperiodic ACFs are derived. Further, it is proved that the sets of combined Frank/Chu codes, which contain a larger number of codes than either of the two constituent sets, also have very good periodic CCFs. Based on Frank codes and Chu codes, two interesting classes of real-valued codes with good correlation properties are defined. It is shown that these codes have periodic complementary properties and good periodic and nonperiodic ACF/CCFs. Finally, a hybrid CCMA/SSMA coding scheme is proposed. This new hybrid coding scheme provides a very flexible and powerful multiple accessing capability and allows simple and efficient decoding. Given an SSMA system with K users and a CCMA system with N users, where at most T users are active at any time, then the hybrid system will have K . N users with at most T.K users active at any time. The hybrid CCMA/SSMA coding scheme is superior to the individual CCMA system or SSMA system in terms of information rate, number of users, decoding complexity and external interference rejection capability.