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In this thesis, we extend applications of Low-Density Parity-Check (LDPC) codes to a combination of constituent sub-channels, which is a mixture of Gaussian channels with erasures. This model, for example, represents a common channel in magnetic recordings where thermal asperities in the system are detected and represented at the decoder as erasures. Although this channel is practically useful, we cannot find any previous work that evaluates performance of LDPC codes over this channel. We are also interested in practical issues such as designing robust LDPC codes for the mixture channel and predicting performance variations due to erasure patterns (random and burst), and finite block lengths. On time varying channels, a common error control strategy is to adapt the coding rate according to available channel state information (CSI). An effective way to realize this coding strategy is to use a single code and puncture it in a rate-compatible fashion, a so-called rate-compatible punctured code (RCPC). We are interested in the existence of good puncturing patterns for rate-changes that minimize performance loss. We show the existence of good puncturing patterns with analysis and verify the results with simulations. Universality of a channel code across a broad range of coding rates is a theoretically interesting topic. We are interested in the possibility of using the puncturing technique proposed in this thesis for designing universal LDPC codes. We also consider how to design high rate LDPC codes by puncturing low rate LDPC codes. The new design method can take advantage of longer effect block lengths, sparser parity-check matrices, and larger minimum distances of low rate LDPC codes.

[pt] Esta dissertação apresenta uma técnica de puncionamento orientada pela polarização para o projeto de códigos polares puncionados. A estratégia de puncionamento proposta consiste em reduzir a matriz geradora relacionando seu índice de linha com o princípio da polarização do canal. Os códigos puncionados construídos com base na polarização do canal são então considerados para a decodificação por cancelamento sucessivos (SC) com os bits perfurados conhecidos tanto no codificador como no decodificador. A Distância de Espectro (SD) e a Distância de Espectro Conjunta (JSD) são então utilizadas para análise de desempenho. Os resultados das simulações mostram que os códigos polares puncionados propostos superam os códigos polares puncionados existentes. / [en] This thesis presents a polarization-driven puncturing technique for the design of punctured polar codes. The proposed puncturing strategy consists of reducing the generator matrix by relating its row index based on the channel polarization principle. The punctured codes constructed based on channel polarization are then considered with successive cancellation (SC) decoding and punctured bits known to both the encoder and the decoder. The Spectrum Distance (SD) and the Joint Spectrum Distance (JSD) are then used to performance analysis. Simulation results show that the proposed punctured polar codes outperform existing punctured polar codes.

This thesis investigates applications of puncturing in error-correction coding and physical layer security with an emphasis on binary and non-binary LDPC codes. Theoretical framework for the analysis of punctured binary LDPC codes at short block lengths is developed and a novel decoding scheme is designed that achieves considerably faster convergence than conventional approaches. Subsequently, optimized puncturing and shortening is studied for non-binary LDPC codes over binary input channels. Framework for the analysis of punctured/shortened non-binary LDPC codes over the BEC channel is developed, which enables the optimization of puncturing and shortening patterns. Insight from this analysis is used to develop algorithms for puncturing and shortening of non-binary LDPC codes at finite block lengths that perform well. It is confirmed that symbol-wise puncturing is generally bad and that bit-wise punctured non-binary LDPC codes can significantly outperform their binary counterparts, thus making them an attractive solution for future communication systems; both for error-correction and distributed compression. Puncturing is also considered in the context of physical layer security. It is shown that puncturing can be used effectively for coding over the wiretap channel to hide the message bits from eavesdroppers. Further, it is shown how puncturing patterns can be optimized for enhanced secrecy. Asymptotic analysis confirms that eavesdroppers are forced to operate at BERs very close to 0.5, even if their signal is only slightly worse than that of the legitimate receivers. The proposed coding scheme is naturally applicable at finite block lengths and allows for efficient, almost-linear time encoding. Finally, it is shown how error-correcting codes can be used to solve an open problem of compressing data encrypted with block ciphers such as AES. Coding schemes for multiple chaining modes are proposed and it is verified that considerable compression gains are attainable for binary sources.

Made available in DSpace on 2014-12-17T14:55:43Z (GMT). No. of bitstreams: 1 AlineFGS_DISSERT.pdf: 1151209 bytes, checksum: 4ae192dd7519e3e14977154f7b70d951 (MD5) Previous issue date: 2010-06-14 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / In this work, a performance analysis of transmission schemes employing turbo trellis coded modulation. In general, the performance analysis of such schemes is guided by evaluating the error probability of these schemes. The exact evaluation of this probability is very complex and inefficient from the computational point of view, a widely used alternative is the use of union bound of error probability, because of its easy implementation and computational produce bounds that converge quickly. Since it is the union bound, it should use to expurge some elements of distance spectrum to obtain a tight bound. The main contribution of this work is that the listing proposal is carried out from the puncturing at the level of symbol rather than bit-level as in most works of literature. The main reason for using the symbol level puncturing lies in the fact that the enummerating function of the turbo scheme is obtained directly from complex sequences of signals through the trellis and not indirectly from the binary sequences that require further binary to complex mapping, as proposed by previous works. Thus, algorithms can be applied through matrix from the adjacency matrix, which is obtained by calculating the distances of the complex sequences of the trellis. This work also presents two matrix algorithms for state reduction and the evaluation of the transfer function of this. The results presented in comparisons of the bounds obtained using the proposed technique with some turbo codes of the literature corroborate the proposition of this paper that the expurgated bounds obtained are quite tight and matrix algorithms are easily implemented in any programming software language / Neste trabalho ? feita uma an?lise de desempenho de esquemas de transmiss?o empregando modula??o codificada turbo em treli?a. Em geral, a an?lise de desempenho de tais esquemas ? guiada pelo c?lculo da probabilidade de erro destes esquemas. O c?lculo exato desta probabilidade ? muito complexo e ineficiente sob o ponto de vista computacional, uma alternativa muito utilizada ? o emprego de limitante da uni?o da probabilidade de erro, por ser de f?cil implementa??o computacional e produzir limitantes que convergem rapidamente. Por se tratar do limitante da uni?o, este deve utilizar de expurgo de alguns elementos do espectro de dist?ncias do c?digo para a obten??o de um limitante apertado. A principal contribui??o deste trabalho ? que a enumera??o proposta ? realizada a partir da perfura??o a n?vel de s?mbolo e n?o a n?vel de bit como na maioria dos trabalhos da literatura. O principal motivo do uso da perfura??o a n?vel de s?mbolo reside no fato que a fun??o enumeradora do esquema turbo ? obtida diretamente das seq??ncias complexas de sinais atrav?s da treli?a e n?o de forma indireta a partir da seq??ncias bin?rias que exigem posterior mapeando bin?rio para complexo, como proposto por trabalhos anteriores. Assim, podem ser aplicados algoritmos completamente matriciais a partir da matriz adjac?ncia, que ? obtida a partir do c?lculo das dist?ncias das seq??ncias complexas da treli?a e n?o das seq??ncias bin?rias. Neste trabalho tamb?m s?o apresentados dois algoritmos matriciais de redu??o de estados do codificador bem como do c?lculo da fun??o de transfer?ncia deste. Os resultados apresentados em forma de compara??es dos limitantes obtidos utilizando a t?cnica proposta com alguns c?digos turbo da literatura corroboram com a proposi??o deste trabalho que os limitantes expurgados obtidos s?o apertados e os algoritmos completamente matriciais s?o facilmente implementados em qualquer software de programa??o simb?lica

Approved for public release; distribution is unlimited / OFDM systems have experienced increased attention in recent years and have found applications in a number of diverse areas including telephone-line based ADSL links, digital audio and video broadcasting systems, and wireless local area networks (WLAN). Orthogonal frequency-division multiplexing (OFDM) is a powerful technique for high data-rate transmission over fading channels. However, to deploy OFDM in a WLAN environment, precise frequency synchronization must be maintained and tricky frequency offsets must be handled. In this thesis, various techniques to improve the data throughput of OFDM WLAN are investigated. A simulation tool was developed in Matlab to evaluate the performance of the IEEE 802.11a physical layer. We proposed a rapid time and frequency synchronization algorithm using only the short training sequence of the IEEE 802.11a standard, thus reducing the training overhead to 50%. Particular attention was paid to channel coding, block interleaving and antenna diversity. Computer simulation showed that drastic improvement in error rate performance is achievable when these techniques are deployed. / Lieutenant, Hellenic Navy

Since the frantic race towards the Shannon bound [1] commenced in the early 1950’s, linear block codes have become integral components of most digital communication systems. Both binary and non-binary linear block codes have proven themselves as formidable adversaries against the impediments presented by wireless communication channels. However, prior to the landmark 1974 paper [2] by Bahl et al. on the optimal Maximum a-Posteriori Probability (MAP) trellis decoding of linear block codes, practical linear block code decoding schemes were not only based on suboptimal hard decision algorithms, but also code-specific in most instances. In 1978 Wolf expedited the work of Bahl et al. by demonstrating the applicability of a block-wise Viterbi Algorithm (VA) to Bahl-Cocke-Jelinek-Raviv (BCJR) trellis structures as a generic optimal soft decision Maximum-Likelihood (ML) trellis decoding solution for linear block codes [3]. This study, largely motivated by code implementers’ ongoing search for generic linear block code decoding algorithms, builds on the foundations established by Bahl, Wolf and other contributing researchers by thoroughly evaluating the VA decoding of popular binary and non-binary linear block codes on realistic narrowband and wideband digital communication platforms in lifelike mobile environments. Ideally, generic linear block code decoding algorithms must not only be modest in terms of computational complexity, but they must also be channel aware. Such universal algorithms will undoubtedly be integrated into most channel coding subsystems that adapt to changing mobile channel conditions, such as the adaptive channel coding schemes of current Enhanced Data Rates for GSM Evolution (EDGE), 3rd Generation (3G) and Beyond 3G (B3G) systems, as well as future 4th Generation (4G) systems. In this study classic BCJR linear block code trellis construction is annotated and applied to contemporary binary and non-binary linear block codes. Since BCJR trellis structures are inherently sizable and intricate, rudimentary trellis complexity calculation and reduction algorithms are also presented and demonstrated. The block-wise VA for BCJR trellis structures, initially introduced by Wolf in [3], is revisited and improved to incorporate Channel State Information (CSI) during its ML decoding efforts. In order to accurately appraise the Bit-Error-Rate (BER) performances of VA decoded linear block codes in authentic wireless communication environments, Additive White Gaussian Noise (AWGN), flat fading and multi-user multipath fading simulation platforms were constructed. Included in this task was the development of baseband complex flat and multipath fading channel simulator models, capable of reproducing the physical attributes of realistic mobile fading channels. Furthermore, a complex Quadrature Phase Shift Keying (QPSK) system were employed as the narrowband communication link of choice for the AWGN and flat fading channel performance evaluation platforms. The versatile B3G multi-user multipath fading simulation platform, however, was constructed using a wideband RAKE receiver-based complex Direct Sequence Spread Spectrum Multiple Access (DS/SSMA) communication system that supports unfiltered and filtered Complex Spreading Sequences (CSS). This wideband platform is not only capable of analysing the influence of frequency selective fading on the BER performances of VA decoded linear block codes, but also the influence of the Multi-User Interference (MUI) created by other users active in the Code Division Multiple Access (CDMA) system. CSS families considered during this study include Zadoff-Chu (ZC) [4, 5], Quadriphase (QPH) [6], Double Sideband (DSB) Constant Envelope Linearly Interpolated Root-of- Unity (CE-LI-RU) filtered Generalised Chirp-like (GCL) [4, 7-9] and Analytical Bandlimited Complex (ABC) [7, 10] sequences. Numerous simulated BER performance curves, obtained using the AWGN, flat fading and multi-user multipath fading channel performance evaluation platforms, are presented in this study for various important binary and non-binary linear block code classes, all decoded using the VA. Binary linear block codes examined include Hamming and Bose-Chaudhuri-Hocquenghem (BCH) codes, whereas popular burst error correcting non-binary Reed-Solomon (RS) codes receive special attention. Furthermore, a simple cyclic binary linear block code is used to validate the viability of employing the reduced trellis structures produced by the proposed trellis complexity reduction algorithm. The simulated BER performance results shed light on the error correction capabilities of these VA decoded linear block codes when influenced by detrimental channel effects, including AWGN, Doppler spreading, diminished Line-of-Sight (LOS) signal strength, multipath propagation and MUI. It also investigates the impact of other pertinent communication system configuration alternatives, including channel interleaving, code puncturing, the quality of the CSI available during VA decoding, RAKE diversity combining approaches and CSS correlation characteristics. From these simulated results it can not only be gathered that the VA is an effective generic optimal soft input ML decoder for both binary and non-binary linear block codes, but also that the inclusion of CSI during VA metric calculations can fortify the BER performances of such codes beyond that attainable by classic ML decoding algorithms. / Dissertation (MEng(Electronic))--University of Pretoria, 2006. / Electrical, Electronic and Computer Engineering / unrestricted