Cyclic codes are a well-known class of linear block codes with efficient decoding algorithms. In recent years they have been generalized to skew-constacyclic codes; such a generalization has previously been shown to be useful. We begin with a study of skew-polynomial rings so that we may examine these codes algebraically as quotient modules of non-commutative skew-polynomial rings. We introduce a skew-generalized circulant matrix to aid in examining skew-constacyclic codes, and we use it to recover a well-known result on the duals of skew-constacyclic codes from Boucher/Ulmer in 2011. We also motivate and develop a notion of idempotent elements in these quotient modules. We are particularly concerned with the existence and uniqueness of idempotents that generate a given submodule; we generalize relevant results from previous work on skew-constacyclic codes by Gao/Shen/Fu in 2013 and well-known results from the classical case.

Codes can be represented by edge-labeled directed graphs called trellises, which are used in decoding with the Viterbi algorithm. We will first examine the well-known product construction for trellises and present an algorithm for recovering the factors of a given trellis. To maximize efficiency, trellises that are minimal in a certain sense are desired. It was shown by Koetter and Vardy that one can produce all minimal tail-biting trellises for a code by looking at a special set of generators for a code. These generators along with a set of spans comprise what is called a characteristic pair, and we will discuss how to determine the number of these pairs for a given code. Finally, we will look at trellis dualization, in which a trellis for a code is used to produce a trellis representing the dual code. The first method we discuss comes naturally with the known BCJR construction. The second, introduced by Forney, is a very general procedure that works for many different types of graphs and is based on dualizing the edge set in a natural way. We call this construction the local dual, and we show the necessary conditions needed for these two different procedures to result in the same dual trellis.

This thesis is concerned with channel estimation and data detection of MIMO-OFDM communication systems using Space-Time Block Coding (STBC) and Space-Frequency Block Coding (SFBC) under frequency selective channels. A new iterative joint channel estimation and signal detection technique for both STBC-OFDM and SFBC-OFDM systems is proposed. The proposed algorithm is based on a processive sequence of events for space time and space frequency coding schemes where pilot subcarriers are used for channel estimation in the first time instant, and then in the second time instant, the estimated channel is used to decode the data symbols in the adjacent data subcarriers. Once data symbols are recovered, the system recursively performs a new channel estimation using the decoded data symbols as pilots. The iterative process is repeated until all MIMO-OFDM symbols are recovered. In addition, the proposed channel estimation technique is based on the maximum likelihood (ML) approach which offers linearity and simplicity of implementation. Due to the orthogonality of STBC and SFBC, high computation efficiency is achieved since the method does not require any matrix inversion for estimation and detection at the receiver. Another major novel contribution of the thesis is the proposal of a new group decoding method that reduces the processing time significantly via the use of sub-carrier grouping for transmitted data recovery. The OFDM symbols are divided into groups to which a set of pilot subcarriers are assigned and used to initiate the channel estimation process. Designated data symbols contained within each group of the OFDM symbols are decoded simultaneously in order to improve the decoding duration. Finally, a new mixed STBC and SFBC channel estimation and data detection technique with a joint iterative scheme and a group decoding method is proposed. In this technique, STBC and SFBC are used for pilot and data subcarriers alternatively, forming the different combinations of STBC/SFBC and SFBC/STBC. All channel estimation and data detection methods for different MIMO-OFDM systems proposed in the thesis have been simulated extensively in many different scenarios and their performances have been verified fully.

Hamming-distance graphs arise naturally in the study of error-correcting codes and have been utilized by several authors to provide new proofs for (and in some cases improve) known bounds on the size of block codes. We study various standard graph properties of the Hamming-distance graphs with special emphasis placed on the chromatic number. A notion of robustness is defined for colorings of these graphs based on the tolerance of swapping colors along an edge without destroying the properness of the coloring, and a complete characterization of the maximally robust colorings is given for certain parameters. Additionally, explorations are made into subgraph structures whose identification may be useful in determining the chromatic number.

Submitted by Eliton Mendonça Moro null (elitonmoro@hotmail.com) on 2017-02-07T16:23:35Z No. of bitstreams: 1 Dissert Moro E M.pdf: 1346120 bytes, checksum: fb365a8ed97b3769301b908d77114d7c (MD5) / Approved for entry into archive by LUIZA DE MENEZES ROMANETTO (luizamenezes@reitoria.unesp.br) on 2017-02-13T16:33:25Z (GMT) No. of bitstreams: 1 moro_em_me_sjrp.pdf: 1346120 bytes, checksum: fb365a8ed97b3769301b908d77114d7c (MD5) / Made available in DSpace on 2017-02-13T16:33:25Z (GMT). No. of bitstreams: 1 moro_em_me_sjrp.pdf: 1346120 bytes, checksum: fb365a8ed97b3769301b908d77114d7c (MD5) Previous issue date: 2017-01-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Os sistemas de comunicação com Múltiplas Entradas e Múltiplas Saídas (MIMO), são sistemas constituídos por estruturas que utilizam várias antenas, tanto no transmissor como no receptor. Por serem transmitidos via antenas, naturalmente surgem problemas de ruídos e de multipercursos, que impõe um desafio para o desenvolvimento dos sistemas de comunicação MIMO. Por esses motivos, muitos estudos focam em certas propriedades dos sinais enviados a fim de minimizar os efeitos sofridos na informação durante a transmissão. Existem muitos tipos diferentes de Códigos de Bloco Espaço-Temporais (STBC) disponíveis para duas antenas transmissoras, dentre eles, o código de bloco espaço-temporal ciclotômico, Código de Ouro e Código de Prata. Neste trabalho apresentamos uma construção de STBC cujos os sinais utilizados na transmissão são identificados por elementos de anéis de inteiros de corpos de números totalmente imaginários, Q(√d), com d<0, e apresentamos os melhores STBC em termos do critério que denominamos como critério produto, considerando extensões de Q(√d) com d=-1,-2,-3,-7, -11. / The communication systems of Multiple Input and Multiple Output (MIMO), are systems consisting of structures that use multiple antennas, both on the transmitter and the receiver. For being transmitted via antennas, noise and path problems naturally arise, which poses a challenge for the development and optimization of MIMO systems. For these reasons, many studies focus on certain properties of the signals sent in order to minimize the effects suffered on the information during transmission. There are many different types of Space-Time Block Codes (STBC) available for two transmitting antennas, such as the cyclotomic space-time block code, Golden code, and Silver code. In this work, we present a STBC construct via totally imaginary quadratic fields, Q(√d) with d <0 and present the best STBC in terms of the criterion that we call product criteria, considering extensions of Q(√d) with d = -1, - 2, - 3, - 7, -11.

In this report, an optical wireless multiple-input multiple-output communication system employing intensity-modulation direct-detection is considered. The performance of direct current offset space-time block codes (DC-STBC) is studied in terms of pairwise error probability (PEP). It is shown that among the class of DC-STBCs, the worst case PEP corresponding to the minimum distance between two codewords is minimized by repetition coding (RC), under both electrical and optical individual power constraints. It follows that among all DC-STBCs, RC is optimal in terms of worst-case PEP for static channels and also for varying channels under any turbulence statistics. This result agrees with previously published numerical results showing the superiority of RC in such systems. It also agrees with previously published analytic results on this topic under log-normal turbulence and further extends it to arbitrary turbulence statistics. This shows the redundancy of the time-dimension of the DCSTBC in this system. This result is further extended to sum power constraints with static and turbulent channels, where it is also shown that the time dimension is redundant, and the optimal DC-STBC has a spatial beamforming structure. Numerical results are provided to demonstrate the difference in performance for systems with different numbers of receiving apertures and different throughput.

The aim of the final Master degree work is to create a method, algorithms and program for cryptographic security of text files. The algorithms of cryptographic security and algorithms aspects are analyzed in the work. Construct program is used for coding / decoding text files using Pseudo – Random Number Generator and it is applied to use in Windows operating system. The program and instructions for its user are formed. The experimental adaption of method and program is done. The program synthesis of coding / decoding text files is described.

We present a new sub-optimal near-maximum-likelihood (ML) detection method for the family of variable-rate space-time block codes (VRSTBC). The proposed detection method is based on the concept of symbol reliability and provides a wide range of performance-complexity trade-offs. The reliability measures are defined with the help of a recent generic ML metric expression. The error performance and complexity analysis of the method via simulations show an achievable near-ML error performance with significant reduction in complexity. The performance of the proposed method is also compared with the group interference cancellation (GIC) method which was the detection method originally applied to VRSTBCs and the results show a significant improvement. The new method offers various levels of error protection via a simple parameter and hence can provide the users of a wireless network with different performance levels according to their cost allowance. Unequal error protection by VRSTBCs under the new detection method was explored. Several applications integrating data with different levels of sensitivity to error can benefit from the wide range of possibilities that the combination of the proposed detection method and VRSTBCs provides. To further explore these flexibilities, four practically interesting power allocation schemes were applied to the transmission and the behaviors were observed through case studies. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2008-09-26 23:45:07.81

The construction of a substitution box (S-box) with high nonlinearity and high resiliency is an important research area in cryptography. In this thesis, t-resilient nxm S-box construction methods depending on linear block codes presented in &quot / A Construction of Resilient Functions with High Nonlinearity&quot / by T. Johansson and E. Pasalic in 2000, and two years later in &quot / Linear Codes in Generalized Construction of Resilient Functions with Very High Nonlinearity&quot / by E. Pasalic and S. Maitra are compared and the former one is observed to be more promising in terms of nonlinearity. The first construction method uses a set of nonintersecting [n-d,m,t+1] linear block codes in deriving t-resilient S-boxes of nonlinearity 2^(n-1)-2^(n-d-1),where d is a parameter to be maximized for high nonlinearity. For some cases, we have found better results than the results of Johansson and Pasalic, using their construction. As a distinguished reference for nxn S-box construction methods, we study the paper &quot / Differentially Uniform Mappings for Cryptography&quot / presented by K.Nyberg in Eurocrypt 1993. One of the two constructions of this paper, i.e., the inversion mapping described by Nyberg but first noticed in 1957 by L. Carlitz and S. Uchiyama, is used in the S-box of Rijndael, which is chosen as the Advanced Encryption Standard. We complete the details of some theorem and proposition proofs given by Nyberg.

The two-antenna problem in aeronautical mobile telemetry is created by the reception of two copies of the same RF waveform with different phases and time delays. Alamouti and Alamouti-like space time block codes can solve the two-antenna problem, but the decoder/detector needs to account for the different time delays between the signals received from the two transmit antennas. In this thesis, a comparison is made between the performance of Alamouti space-time block codes and time-reversed space-time block codes with 16-APSK to solve the two-antenna problem. The maximum likelihood decoder/detector for Alamouti-encoded 16-APSK is a sequence detector operating on a trellis with a large number of states. A practical state-reduction technique is presented. The results produce a trellis with 256 states and a small loss in bit error rate performance as long as the delay difference is not too big. The decoder/detector for the time-reversed space time block requires only waveform manipulations and channel matched filtering in the case where the two channels are simple delays. For the more general case of multipath propagation between the two transmit antennas and the receiver, the decoder/detector requires an equalizer; simulation results using a channel pair measured at a test range show that the decoder/detector is capable of achieving near AWGN performance with a modest equalizer.