Balanced Incomplete Block Designs and Binary Linear Codes are two combinatorial designs. Due to the vast application of codes in communication the field of coding theory progressed more rapidly than many other fields of combinatorial designs. On the other hand, Block Designs are applicable in statistics and designing experiments in different fields, such as biology, medicine, and agriculture. Finding the relationship between instances of these two designs can be useful in constructing instances of one from the other. Applying the properties of codes to corresponding instances of Balanced Incomplete Block Designs has been used previously to show the non-existence of some designs. In this research the relationship between (16,6,3)-designs and (25,12) codes was determined.

<p>In the high-end research process of wireless systems and in the race for the development of the new technologies, MIMO (Multiple Input, Multiple Output) is getting more attention now days. It has a high potential usage in the 3G and 4G communications and beyond. The MIMO based system has got the ability to increase the data throughput in spectrum-limited conditions. With the increase and complexity of wireless applications, the spectrum efficiency improvement in the physical layer will be saturated. MIMO is predicted to be one of the major features for the next generation wireless networking. This thesis work is a part of an ongoing project of the Generic MIMO decoder design carried out at the research laboratory, LESTER at Lorient, France. I was involved in the study of MIMO concepts, orthogonal and Space-time codes and later involved in the design and optimization of the architecture for the core operator for the ML decoder used in the reception of the MIMO system,which is presented in this report work.</p>

In the high-end research process of wireless systems and in the race for the development of the new technologies, MIMO (Multiple Input, Multiple Output) is getting more attention now days. It has a high potential usage in the 3G and 4G communications and beyond. The MIMO based system has got the ability to increase the data throughput in spectrum-limited conditions. With the increase and complexity of wireless applications, the spectrum efficiency improvement in the physical layer will be saturated. MIMO is predicted to be one of the major features for the next generation wireless networking. This thesis work is a part of an ongoing project of the Generic MIMO decoder design carried out at the research laboratory, LESTER at Lorient, France. I was involved in the study of MIMO concepts, orthogonal and Space-time codes and later involved in the design and optimization of the architecture for the core operator for the ML decoder used in the reception of the MIMO system,which is presented in this report work.

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The presented work considers a CDMA-based Wireless Body Area Network (WBAN) where multiple biosensors communicate simultaneously to a central node in an asynchronous fashion. The asynchronous nature of the WBAN introduces Multiple Access Interference (MAI). To combat this problem, presented is a methodology that uses a set of cyclically orthogonal spreading codes extracted from the Walsh-Hadamard matrix. When using the Cyclic Orthogonal Walsh-Hadamard Codes (COWHC) as spreading codes in the CDMA-based WBAN, the cyclic orthogonality property helps mitigate MAI amongst the on-body sensors. Presented is an ideal communication system that is most effective at mitigating MAI in proactive WBANs. The work illustrates the system optimality and effectiveness at mitigating MAI by studying the sensitivity to packet-loss through simulating the link Bit Error Rate (BER) performance. It is shown that the proposed design with COWHC, a Rayleigh flat-fading channel, BPSK modulation and a conventional receiver produce optimum MAI mitigation.

The presented work considers a CDMA-based Wireless Body Area Network (WBAN) where multiple biosensors communicate simultaneously to a central node in an asynchronous fashion. The asynchronous nature of the WBAN introduces Multiple Access Interference (MAI). To combat this problem, presented is a methodology that uses a set of cyclically orthogonal spreading codes extracted from the Walsh-Hadamard matrix. When using the Cyclic Orthogonal Walsh-Hadamard Codes (COWHC) as spreading codes in the CDMA-based WBAN, the cyclic orthogonality property helps mitigate MAI amongst the on-body sensors. Presented is an ideal communication system that is most effective at mitigating MAI in proactive WBANs. The work illustrates the system optimality and effectiveness at mitigating MAI by studying the sensitivity to packet-loss through simulating the link Bit Error Rate (BER) performance. It is shown that the proposed design with COWHC, a Rayleigh flat-fading channel, BPSK modulation and a conventional receiver produce optimum MAI mitigation.

In this thesis, we investigate in detail, certain important problems in cryptography and coding theory. In the first part of this thesis, we discuss the number field sieve and compare the two ways in which the sieving step is implemented -one method using the line sieve and the other using the lattice sieve. We discuss why the lattice sieve performs better than the line sieve in the presence of large primes -this has not been attempted before. In the second part of this thesis, we design low-correlation CDMA sequences over the Quadrature Amplitude Modulation (QAM) alphabet. The sequences proposed in this thesis have the lowest value of the maximum correlation parameter as compared to any other family in the literature. In the third part of this thesis, we design large families of optimal two-dimensional optical orthogonal codes for optical CDMA. The size of these codes is larger than any other code in the literature.

The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. Despite the large body of literature in quantum coding theory, many important questions, especially those centering on the issue of "good codes" are unresolved. In this dissertation the dominant underlying theme is that of constructing good quantum codes. It approaches this problem from three rather different but not exclusive strategies. Broadly, its contribution to the theory of quantum error correction is threefold. Firstly, it extends the framework of an important class of quantum codes - nonbinary stabilizer codes. It clarifies the connections of stabilizer codes to classical codes over quadratic extension fields, provides many new constructions of quantum codes, and develops further the theory of optimal quantum codes and punctured quantum codes. In particular it provides many explicit constructions of stabilizer codes, most notably it simplifies the criteria by which quantum BCH codes can be constructed from classical codes. Secondly, it contributes to the theory of operator quantum error correcting codes also called as subsystem codes. These codes are expected to have efficient error recovery schemes than stabilizer codes. Prior to our work however, systematic methods to construct these codes were few and it was not clear how to fairly compare them with other classes of quantum codes. This dissertation develops a framework for study and analysis of subsystem codes using character theoretic methods. In particular, this work established a close link between subsystem codes and classical codes and it became clear that the subsystem codes can be constructed from arbitrary classical codes. Thirdly, it seeks to exploit the knowledge of noise to design efficient quantum codes and considers more realistic channels than the commonly studied depolarizing channel. It gives systematic constructions of asymmetric quantum stabilizer codes that exploit the asymmetry of errors in certain quantum channels. This approach is based on a Calderbank- Shor-Steane construction that combines BCH and finite geometry LDPC codes.

[pt] Este trabalho apresenta uma análise detalhada de uma recente proposta de combinação da transmissão em blocos com portadora única e a técnica CDMA, referida como CS-CDMA (Chip Spread CDMA). Uma característica marcante desta técnica de transmissão é que diferentemente do que ocorre nos sistemas DS-CDMA, a ortogonalidade entre os códigos dos diferentes usuários é mantida mesmo quando a transmissão é feita através de um canal multipercurso seletivo em frequência, suposto invariante no tempo, permitindo assim que os usuários possam ser identicamente desacoplados na recepção. Além desta vantagem, resultados de desempenho indicaram uma significativa superioridade deste sistema sobre o tradicional DS-CDMA. Entretanto comparações existentes, consideraram apenas o up-link, do sistema e adotaram algumas premissas, que incluem, a utilização de códigos ortogonais pelos diversos usuários e a suposição de canais de transmissão invariantes no tempo. O presente trabalho apresenta uma análise detalhada da técnica (CS-CDMA e uma análise comparativa dos sistemas em condições menos favoráveis. Os sistemas operam em ambientes invariante e variante no tempo, com códigos ortogonais e não ortogonais e em dois cenários diferentes, down- link e up-link. Os resultados consideram recepção com equalização no domínio da frequência utilizando equalizadores do tipo ZF (Zero Forcing) e MMSE (Minimum Mean Squared Error). Simulações foram realizadas no intuito de se avaliar o desempenho dos dois sistemas considerados. Curvas de probabilidade de erro foram obtidas e ilustram e comparam tais desempenhos em diferentes situações e cenários de interesse. / [en] This dissertation proposes detailed analysis of a recent combined mechanism for transmission in blocks with a single carrier and CDMA technique known as Chip Spread CDMA (CS-CDMA). An important feature of this transmission technique is that unlike what happens in Direct Sequence (DS-CDMA) systems, the orthogonality between codes of different users is maintained even when the transmission, considered time-invariant, is made through a selective multipath channel frequency, which ideally allows users to be uncoupled in reception. However, existing comparisons only consider the up-link transmission and adopt certain assumptions, which include orthogonal codes for different users and time invariant channels. This technique have shown a significant superiority as compared with the traditional DS-CDMA. A comparison of (CS-CDMA systems in more realistic conditions are presented in this work. Various environments were tested in the presence of BPSK modulation systems, as well as invariant and time-varying transmission. Comparison between scenarios down-link and up-link are also presented. The results consider equalized reception in the frequency domain using the ZF (Zero Forcing) equalizers and MMSE (Minimum Mean Squared Error). Simulations were carried out in order to evaluate the performance of the two systems considered. Error probability curves were obtained to illustrate and compare the performances in different situations and scenarios.