Near lossless source coding with side information only at the decoder, was first considered by Slepian and Wolf in 1970s, and rediscovered recently due to applications such as sensor network and distributed video coding. Suppose X is a source and Y is the side information. The coding scheme proposed by Slepian and Wolf, called SW coding, in which information only flows from the encoder to the decoder, was shown to achieve the rate H(X|Y) asymptotically for stationary ergodic source pairs, but not for non-ergodic case, shown by Yang and He. Recently, a new source coding paradigm called interactive encoding and decoding(IED) was proposed for near lossless coding with side information only at the decoder, where information flows in both ways, from the encoder to the decoder and vice verse. The results by Yang and He show that IED schemes are much more appealing than SW coding schemes to applications where the interaction between the encoder and the decoder is possible. However, the IED schemes proposed by Yang and He do not have an intrinsic structure that is amenable to design and implement in practice. Towards practical design, we restrict the encoding method to linear block codes, resulting in linear IED schemes. It is then shown that this restriction will not undermine the asymptotical performance of IED. Another step of practical design of IED schemes is to make the computational complexity incurred by encoding and decoding feasible. In the framework of linear IED, a scheme can be conveniently described by parity check matrices. Then we get an interesting trade-off between the density of the associated parity check matrices and the resulting symbol error probability. To implement the idea of linear IED and follow the instinct provided by the result above, Low Density Parity Check(LDPC) codes and Belief Propagation(BP) decoding are utilized. A successive LDPC code is proposed, and a new BP decoding algorithm is proposed, which applies to the case where the correlation between $Y$ and $X$ can be modeled as a finite state channel. Finally, simulation results show that linear IED schemes are indeed superior to SW coding schemes.

Near lossless source coding with side information only at the decoder, was first considered by Slepian and Wolf in 1970s, and rediscovered recently due to applications such as sensor network and distributed video coding. Suppose X is a source and Y is the side information. The coding scheme proposed by Slepian and Wolf, called SW coding, in which information only flows from the encoder to the decoder, was shown to achieve the rate H(X|Y) asymptotically for stationary ergodic source pairs, but not for non-ergodic case, shown by Yang and He. Recently, a new source coding paradigm called interactive encoding and decoding(IED) was proposed for near lossless coding with side information only at the decoder, where information flows in both ways, from the encoder to the decoder and vice verse. The results by Yang and He show that IED schemes are much more appealing than SW coding schemes to applications where the interaction between the encoder and the decoder is possible. However, the IED schemes proposed by Yang and He do not have an intrinsic structure that is amenable to design and implement in practice. Towards practical design, we restrict the encoding method to linear block codes, resulting in linear IED schemes. It is then shown that this restriction will not undermine the asymptotical performance of IED. Another step of practical design of IED schemes is to make the computational complexity incurred by encoding and decoding feasible. In the framework of linear IED, a scheme can be conveniently described by parity check matrices. Then we get an interesting trade-off between the density of the associated parity check matrices and the resulting symbol error probability. To implement the idea of linear IED and follow the instinct provided by the result above, Low Density Parity Check(LDPC) codes and Belief Propagation(BP) decoding are utilized. A successive LDPC code is proposed, and a new BP decoding algorithm is proposed, which applies to the case where the correlation between $Y$ and $X$ can be modeled as a finite state channel. Finally, simulation results show that linear IED schemes are indeed superior to SW coding schemes.

In orthogonal frequency division multiplexing (OFDM) system, blind estimator was proposed which can obtain high bandwidth efficiently. There is a serious ambiguity problem in blind data detector structure. Solution methods can divide into three cases: pilot signal, superimposed training, and channel coding. In order to achieve totally blind estimate, we use channel coding to solve ambiguity in this thesis. In previous study, it had been use low-density-parity-check code (LDPC) to solve ambiguity, and proposed an encoding method to avoid ambiguity for BPSK. However, we consider generic linear block code (LBC) and want to extend BPSK modulation to higher modulation scheme, including QPSK, 16QAM, and 64QAM. For any constellation follows grey coding, we induct a difference of inner product for ambiguity and derive some sufficient conditions for LBC. If LBC satisfy some conditions, then it could avoid ambiguity between valid code words and it can achieve totally blind estimate. In simulation section, for data estimate, we respectively use two LBC cases, which exist ambiguity or not. In order to be fair, we insert a pilot to solve ambiguity in LBC, which exist ambiguity. In simulation results, the performance of two cases is similar in high signal to noise ratio (SNR). In other words, if we use proper channel code which it satisfy sufficient conditions, then we can increase bandwidth efficiently.

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