Error control coding is frequently used to minimise the errors which occur naturally in the transmission and storage of digital data. Many methods for decoding such codes already exist. The choice falls mainly into two areas: hard-decision algebraic decoding, a computationally-efficient method, and soft-decision combinatorial decoding, which although more complex offers better error-correction. The work presented in this Thesis is intended to provide practical decoding algorithms which can be implemented in real systems. Soft-decision maximum-likelihood decoding of Reed-Solomon codes can be obtained by using the Viterbi algorithm over a suitable trellis. Two-stage decoding of Reed-Solomon codes is presented. It is an algorithm by which near-optimum performance may be achieved with a complexity lower than the Viterbi algorithm. The soft-output Viterbi algorithm (SOVA) has been investigated as a means of providing soft-decision information for subsequent decoders. Considerations of how to apply SOVA to multi-level codes are given. The use of SOVA in a satellite downlink channel is discussed. The results of a computer simulation, which showed a 1.8dB improvement in coding gain for only a 20% increase in decoding complexity, are presented. SOVA was also used to improve the decoding performance when applied to an RS product code. Several different decoding methods were evaluated, including cascade decoding, and a method where the row and columns were decoded alternately. A complexity measurement was developed which allows accurate comparisons of decoding complexity for trellis-based and algebraic decoders. With this technique the decoding complexity of all the algorithms implemented are compared. Also included in the comparison are the Euclidean and Berlekamp-Massey algorithms.

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Data compression, the reduction in size of the physical representation of data being stored or transmitted, has long been of interest both as a research topic and as a practical technique. Different methods are used for encoding different classes of data files. The purpose of this research is to compress a class of highly redundant data files whose contents are partially described by a context-free grammar (i.e. text files containing computer programs). An encoding technique is developed for the removal of structural dependancy due to the context-free structure of such files. The technique depends on a type of LR parsing method called LALR(K) (Lookahead LRM). The encoder also pays particular attention to the encoding of editing characters, comments, names and constants. The encoded data maintains the exact information content of the original data. Hence, a decoding technique (depending on the same parsing method) is developed to recover the original information from its compressed representation. The technique is demonstrated by compressing Pascal programs. An optimal coding scheme (based on Huffman codes) is used to encode the parsing alternatives in each parsing state. The decoder uses these codes during the decoding phase. Also Huffman codes, based on the probability of the symbols c oncerned, are used when coding editing characterst comments, names and constants. The sizes of the parsing tables (and subsequently the encoding tables) were considerably reduced by splitting them into a number of sub-tables. The minimum and the average code length of the average program are derived from two different matrices. These matrices are constructed from a probabilistic grammar, and the language generated by this grammar. Finally, various comparisons are made with a related encoding method by using a simple context-free language.

In the last two decades or so there has been great interest in the problem of estimating signal parameters from the measurements at sensor array outputs. The most important parameters are probably the directions-of-arrival (DOAs) at the array from radiating sources in the observed spatial field. This thesis is devoted to the study of algorithms and techniques which have been suggested from different points of view for the same direction estimation problem. Several classes of algorithms are examined which include the conventional beamforming methods, eigenstructure based algorithms, subspace rotation methods, decompositions techniques, and the more recently proposed weighted subspace fitting methods. The research in this thesis contains three main aspects addressing theoretical analyses, computer simulations, and practical experiments respectively. A set of simulation programs has been developed to evaluate the performance in various scenarios, and Monte Carlo tests have been carried out to support theoretical analyses. The simulation work was carried out on an IBM PC, and the computer language used was MATLAB (Matrix Laboratory), a package especially developed for matrix computations. A sonar system available in the sonar research group at Loughborough University of Technology (LUT) was modified and used to collect real data for off-line processing so as to demonstrate the algorithm performance in real experimental environments. Two scenarios were examined when the system worked in passive and active modes respectively. In the passive working mode, two emitters were employed to give uncorrelated or strongly correlated signals by using the same or different working frequencies. When working in the active mode, a single sensor was placed on the top of the receiving array which received reflections from two targets in the distance. The data was captured and then saved on floppy disks from the measurement system and processed on PCs. A large number of results are presented, analysed, and summarized in the thesis, including· both computer simulations and practical measurements. This provides a fundamental ground for further work in this and related areas.

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Using speech transmission via a telephone channel of bandwidth 0.3 to 3.4 kHz, it is desired to gain a wider subjective bandwidth at the receiver output than that afforded by the channel itself. The channel is considered here to be a realisable perfect band pass filter, i.e. free of noise or dispersion.

Differential pulse-code modulation (DPCM) is an efficient digitization technique for encoding speech signals. The two principal components of a DPCM system are the quantizer and the predictor, either or both of which can be adaptive. This thesis describes the investigation of various differential pulse-code modulation systems. Initially, fixed, i.e. time-invariant, predictors using long-term signal statistics of the speech signal are examined. The performance of such a predictor in a DPCM system having a fixed quantizer is studied. Then by replacing the fixed predictor with one whose coefficients are calculated at fixed time intervals, the performance of the encoder, in terms of signal to noise ratio (SNR), is improved by 3-5 dB. A further improvement of 2–3 dB in SNR is obtained when an adaptive quantizer is used in the DPCM system. However, the block adaptive predictor requires the transmission of prediction coefficients to the receiving end at the expense of an increase in the channel band width.

When digital data is transmitted over a noisy channel, there is always a chance that the received data will contain errors. Usually an error rate is specified above which the received data is considered unusable, and if the channel error rate exceeds this value then error correction coding can be used to reduce the error rate to an acceptable level.

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This thesis aims to examine those factors which affect the quality and performance of low bit-rate coding algorithms for speech, based on linear prediction, operating between 4-16kb/s. While coding algorithms at 64kb/s and 32kb/s are now accepted CCITT standards, and a similar standard will be shortly adopted at 16kb/s, speech coding systems operating below these rates are not yet in wide-spread use, except for one or two specific systems such as GSM. Yet low bit-rate digital speech systems will become an essential part of many of the proposed mobile networks, based on both cellular and satellite technology. Of several possible candidates for low bit-rate applications, it is linear predictive coders that appear to offer the best in terms of quality and efficiency, and many developments, based on linear prediction, have been reported in the literature over the past twenty years. What is less clear is whether there is the potential for linear predictive coders to be developed further with better quality at even lower rates. This thesis sets out to examine some of those issues. The first part of the thesis develops a general theory for speech coding in terms of a hierarchical model of speech communication and identifies a dual function in the redundancies that exist at each layer of the hierarchical structure. The operation of linear predictive coding, in terms of this model is described, and it is shown that the limits to performance are determined by the ability of the encoder to efficiently transfer communication from a lower to a higher level in the hierarchy. The thesis then turns its attention towards the specific performance of linear prediction analysis on speech signals. It is shown that there is a limit to the performance that can be obtained with conventional linear prediction analysis due to the assumptions upon which the theory of linear prediction is based. A range of sub-classes of linear predictive coder are then compared in terms of the general model and the analysis procedures in the encoder stage are identified as being the key to coder performance. The central part of this thesis examines, specifically, a range of pitch determination algorithms which may be employed to enable accurate extraction of pitch correlations from the speech signal. A number of candidates are identified and compared. An investigation into the robustness of these algorithms to noisy speech is presented and a new highly robust algorithm is described. Finally, an investigation into robust linear prediction is reported. This falls into two parts - the performance of linear prediction on noisy speech and the performance of linear prediction during voiced speech. A range of methods for improving linear prediction during voiced speech are compared and the recently proposed method of Lee is examined in depth. Results of the application of Lee's method to speech coding is given and an improved version of the algorithm is described.