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Asynchronous multiplexing schemes are efficient than synchronous schemes, in a bursty traffic environment of multiple access local area network (LAN), as fixed bandwidth is not allocated among the users and there is no access delay. Fiber- Optic Code-Division Multiple Access (FO-CDMA) is one such asynchronous multiplexing scheme suitable for high speed LAN networks. While FO-CDMA offers potential benefits it also faces challenges in three diverse areas which are 1) coding algorithms and schemes 2) advanced encoding and decoding hardware and 3) network architecture. In this thesis, as a solution to the first challenge, we propose the design and construction of a new family of codes, wavelength/time multiple-pulses-per-row (W/T MPR) codes. These codes have good cardinality, spectral efficiency and minimal cross-correlation values. Performance analysis of the W/T MPR codes is carried out and found to be superior to other codes. In unipolar 1-D Optical Orthogonal Codes (OOCs) proposed by Salehi et al., the ratio of code length/code weight grows rapidly as the number of users is increased for a reasonable weight. Hence, for a given pulse width, the data rate decreases or in other words for a given data rate very narrow pulses have to be used, because of which dispersion effects will be dominant. To overcome the drawbacks of non-linear effects in large spread sequences of 1-D unipolar codes in FO-CDMA networks, several two-dimensional codes have been proposed. Wavelength-time (W/T) encoding of the two-dimensional codes is practical in FO-CDMA networks. W/T codes reported so far can be classified mainly into two types: 1) hybrid sequences, where one type of sequence is crossed with another to improve the cardinality and correlation properties and 2) matrix codes, 1-D sequences converted to 2-D codes or 2-D codes by construc- tion, to reduce the ’time’ spread of the sequences/codes. Prime-hop and eqc/prime W/T hybrid codes have been proposed where one type of sequence is crossed with another to improve the cardinality and correlation properties. Other constructions deal with conversion of 1-D sequences to 2-D codes either by using Chinese remainder theorem or folding GoLomb rulers. W/T single-pulse-per-row (W/T SPR) codes are 2-D codes constructed using algebraic method Addition Modulo Group operation. Motivation for this work: To design a family of 2-D codes which have the design choice of length of one dimension over the other, and also have better cardinality, spectral efficiency and also low cross-correlation values (thereby have low BER) than that of the reported unipolar 2-D codes. In this thesis, we describe the design principles of W/T MPR codes, for in- coherent FO-CDMA networks, which have good cardinality, spectral efficiency and minimal cross-correlation values. Another feature of the W/T MPR codes is that the aspect ratio can be varied by trade off between wavelength and temporal lengths. We lay down the necessary conditions to be satisfied by W/T MPR codes to have minimal correlation values of unity. We analytically prove the correlation results and also verify by simulation (of the codes) using Matlab software tool. We also discuss the physical implementation of the W/T MPR FO-CDMA network with optical encoding and decoding. We show analytically that when distinct 1-D OOCs of a family are used as the row vectors of a W/T MPR code, it will have off-peak autocorrelation equal to ‘1’. An expression for the upper bound on the cardinality of W/T MPR codes is derived. We also show that 1-D OOCs and W/T SPR codes are the limiting cases of W/T MPR codes. Starting with distinct 1-D OOCs, of a family, as row vectors, we propose a greedy algorithm, for the construction of W/T MPR codes and present the repre- sentations of the results. An entire W/T MPR code family, generated using greedy algorithm, is simulated for various number of interfering users. Performance analysis of the W/T MPR codes and their limiting cases is carried out for various parameter variations such as the dimensions of wavelength, time and weight of the code. We evaluate the performance in terms of BER, capacities of the networks, temporal lengths needed (to achieve a given BER). Multiple access interference (MAI) signal can be reduced, by using a bistable optical hard-limiter device in the W/T MPR code receiver, by eliminating those signal levels which exceed a certain preset level. Performance analysis of the W/T MPR codes and their limiting cases is studied for various parameter variations. For given wavelength × time dimensions, we compare various W/T codes, whose cardinalities are known, and show that W/T MPR family of codes have better cardinality and spectral efficiency than the other (reported) W/T codes. As W/T MPR codes are superior to other W/T codes in terms of cardinality, spectral efficiency, low peak cross-correlation values and at the same time have good performance, makes it a suitable coding scheme for incoherent FO-CDMA access networks.

One of the most popular ways to exploit the advantages of a multiple-input multiple-output (MIMO) system is using space time block coding. A space time block code (STBC) is a finite set of complex matrices whose entries consist of the information symbols to be transmitted. A linear STBC is one in which the information symbols are linearly combined to form a two-dimensional code matrix. A well known method of maximum-likelihood (ML) decoding of such STBCs is using the sphere decoder (SD). In this thesis, new constructions of STBCs with low sphere decoding complexity are presented and various ways of characterizing and reducing the sphere decoding complexity of an STBC are addressed. The construction of low sphere decoding complexity STBCs is tackled using irreducible matrix representations of Clifford algebras, cyclic division algebras and crossed-product algebras. The complexity reduction algorithms for the STBCs constructed are explored using tree based search algorithms. Considering an STBC as a vector space over the set of weight matrices, the problem of characterizing the sphere decoding complexity is addressed using quadratic form representations. The main results are as follows. A sub-class of fast decodable STBCs known as Block Orthogonal STBCs (BOSTBCs) are explored. A set of sufficient conditions to obtain BOSTBCs are explained. How the block orthogonal structure of these codes can be exploited to reduce the SD complexity of the STBC is then explained using a depth first tree search algorithm. Bounds on the SD complexity reduction and its relationship with the block orthogonal structure are then addressed. A set of constructions to obtain BOSTBCs are presented next using Clifford unitary weight designs (CUWDs), Coordinate-interleaved orthogonal designs (CIODs), cyclic division algebras and crossed product algebras which show that a lot of codes existing in literature exhibit the block orthogonal property. Next, the dependency of the ordering of information symbols on the SD complexity is discussed following which a quadratic form representation known as the Hurwitz-Radon quadratic form (HRQF) of an STBC is presented which is solely dependent on the weight matrices of the STBC and their ordering. It is then shown that the SD complexity is only a function of the weight matrices defining the code and their ordering, and not of the channel realization (even though the equivalent channel when SD is used depends on the channel realization). It is also shown that the SD complexity is completely captured into a single matrix obtained from the HRQF. Also, for a given set of weight matrices, an algorithm to obtain a best ordering of them leading to the least SD complexity is presented using the HRQF matrix.