Code design and analysis for multiple access communications

This thesis explores various coding aspects of multiple access communications, mainly for spread spectrum multiaccess(SSMA) communications and collaborative coding multiaccess(CCMA) communications. Both the SSMA and CCMA techniques permit efficient simultaneous transmission by several users sharing a common channel, without subdivision in time or frequency. The general principle behind these two multiaccess schemes is that one can find sets of signals (codes) which can be combined together to form a composite signal; on reception, the individual signals in the set can each be recovered from the composite signal. For the CCMA scheme, the isolation between users is based on the code structure; for the SSMA scheme, on the other hand, the isolation between users is based on the autocorrelation functions(ACFs) and crosscorrelation functions (CCFs) of the code sequences. It is clear that, in either case, the code design is the key to the system design.For the CCMA system with a multiaccess binary adder channel, a class of superimposed codes is analyzed. It is proved that every constant weight code of weight w and maximal correlation λ corresponds to a subclass of disjunctive codes of order T 3, the out-of-phase ACFs and CCFs of the codes are constant and equal to √L. In addition, all codes of the same length are mutually orthogonal.2. Maximal length sequences (m-sequences) over Gaussian integers, suitable for use with QAM modulation, are considered. Two sub-classes of m-sequences with quasi-perfect periodic autocorrelations are obtained. The CCFs between the decimated m-sequences are studied. By applying a simple operation, it is shown that some m-sequences over rational and Gaussian integers can be transformed into perfect sequences with impulsive ACFs.3. Frank codes and Chu codes have perfect periodic ACFs and optimum periodic CCFs. In addition, it is shown that they also have very favourable nonperiodic ACFs; some new results concerning the behaviour of the nonperiodic ACFs are derived. Further, it is proved that the sets of combinedFrank/Chu codes, which contain a larger number of codes than either of the two constituent sets, also have very good periodic CCFs. Based on Frank codes and Chu codes, two interesting classes of real-valued codes with good correlation properties are defined. It is shown that these codes have periodic complementary properties and good periodic and nonperiodic ACF/CCFs.Finally, a hybrid CCMA/SSMA coding scheme is proposed. This new hybrid coding scheme provides a very flexible and powerful multiple accessing capability and allows simple and efficient decoding. Given an SSMA system with K users and a CCMA system with N users, where at most T users are active at any time, then the hybrid system will have K . N users with at most T.K users active at any time. The hybrid CCMA/SSMA coding scheme is superior to the individual CCMA system or SSMA system in terms of information rate, number of users, decoding complexity and external interference rejection capability

Code design and analysis for multiple access communications

This thesis explores various coding aspects of multiple access communications, mainly for spread spectrum multiaccess(SSMA) communications and collaborative coding multiaccess(CCMA) communications. Both the SSMA and CCMA techniques permit efficient simultaneous transmission by several users sharing a common channel, without subdivision in time or frequency. The general principle behind these two multiaccess schemes is that one can find sets of signals (codes) which can be combined together to form a composite signal; on reception, the individual signals in the set can each be recovered from the composite signal. For the CCMA scheme, the isolation between users is based on the code structure; for the SSMA scheme, on the other hand, the isolation between users is based on the autocorrelation functions(ACFs) and crosscorrelation functions (CCFs) of the code sequences. It is clear that, in either case, the code design is the key to the system design.For the CCMA system with a multiaccess binary adder channel, a class of superimposed codes is analyzed. It is proved that every constant weight code of weight w and maximal correlation λ corresponds to a subclass of disjunctive codes of order T 3, the out-of-phase ACFs and CCFs of the codes are constant and equal to √L. In addition, all codes of the same length are mutually orthogonal.2. Maximal length sequences (m-sequences) over Gaussian integers, suitable for use with QAM modulation, are considered. Two sub-classes of m-sequences with quasi-perfect periodic autocorrelations are obtained. The CCFs between the decimated m-sequences are studied. By applying a simple operation, it is shown that some m-sequences over rational and Gaussian integers can be transformed into perfect sequences with impulsive ACFs.3. Frank codes and Chu codes have perfect periodic ACFs and optimum periodic CCFs. In addition, it is shown that they also have very favourable nonperiodic ACFs; some new results concerning the behaviour of the nonperiodic ACFs are derived. Further, it is proved that the sets of combinedFrank/Chu codes, which contain a larger number of codes than either of the two constituent sets, also have very good periodic CCFs. Based on Frank codes and Chu codes, two interesting classes of real-valued codes with good correlation properties are defined. It is shown that these codes have periodic complementary properties and good periodic and nonperiodic ACF/CCFs.Finally, a hybrid CCMA/SSMA coding scheme is proposed. This new hybrid coding scheme provides a very flexible and powerful multiple accessing capability and allows simple and efficient decoding. Given an SSMA system with K users and a CCMA system with N users, where at most T users are active at any time, then the hybrid system will have K . N users with at most T.K users active at any time. The hybrid CCMA/SSMA coding scheme is superior to the individual CCMA system or SSMA system in terms of information rate, number of users, decoding complexity and external interference rejection capability

On Multiple Decoding Attempts for Reed-Solomon Codes: A Rate-Distortion Approach

One popular approach to soft-decision decoding of Reed-Solomon (RS) codes is based on using multiple trials of a simple RS decoding algorithm in combination with erasing or flipping a set of symbols or bits in each trial. This paper presents a framework based on rate-distortion (RD) theory to analyze these multiple-decoding algorithms. By defining an appropriate distortion measure between an error pattern and an erasure pattern, the successful decoding condition, for a single errors-and-erasures decoding trial, becomes equivalent to distortion being less than a fixed threshold. Finding the best set of erasure patterns also turns into a covering problem which can be solved asymptotically by rate-distortion theory. Thus, the proposed approach can be used to understand the asymptotic performance-versus-complexity trade-off of multiple errors-and-erasures decoding of RS codes. This initial result is also extended a few directions. The rate-distortion exponent (RDE) is computed to give more precise results for moderate blocklengths. Multiple trials of algebraic soft-decision (ASD) decoding are analyzed using this framework. Analytical and numerical computations of the RD and RDE functions are also presented. Finally, simulation results show that sets of erasure patterns designed using the proposed methods outperform other algorithms with the same number of decoding trials.Comment: to appear in the IEEE Transactions on Information Theory (Special Issue on Facets of Coding Theory: from Algorithms to Networks

Easily decoded error correcting codes

This thesis is concerned with the decoding aspect of linear block error-correcting codes. When, as in most practical situations, the decoder cost is limited an optimum code may be inferior in performance to a longer sub-optimum code' of the same rate. This consideration is a central theme of the thesis. The best methods available for decoding short optimum codes and long B.C.H. codes are discussed, in some cases new decoding algorithms for the codes are introduced. Hashim's "Nested" codes are then analysed. The method of nesting codes which was given by Hashim is shown to be optimum - but it is seen that the codes are less easily decoded than was previously thought. "Conjoined" codes are introduced. It is shown how two codes with identical numbers of information bits may be "conjoined" to give a code with length and minimum distance equal to the sum of the respective parameters of the constituent codes but with the same number of information bits. A very simple decoding algorithm is given for the codes whereby each constituent codeword is decoded and then a decision is made as to the correct decoding. A technique is given for adding more codewords to conjoined codes without unduly increasing the decoder complexity. Lastly, "Array" codes are described. They are formed by making parity checks over carefully chosen patterns of information bits arranged in a two-dimensional array. Various methods are given for choosing suitable patterns. Some of the resulting codes are self-orthogonal and certain of these have parameters close to the optimum for such codes. A method is given for adding more codewords to array codes, derived from a process of augmentation known for product codes

Versatile Error-Control Coding Systems

$NC research reported in this thesis is in the field of error-correcting codes, which has evolved as a very important branch of information theory. The main use of error-correcting codes is to increase the reliability of digital data transmitted through a noisy environment. There are, sometimes, alternative ways of increasing the reliability of data transmission, but coding methods are now competitive in cost and complexity in many cases because of recent advances in technology. The first two chapters of this thesis introduce the subject of error-correcting codes, review some of the published literature in this field and discuss the advan­tages of various coding techniques. After presenting linear block codes attention is from then on concentrated on cyclic codes, which is the subject of Chapter 3. The first part of Chapter 3 presents the mathemati­cal background necessary for the study of cyclic codes and examines existing methods of encoding and their practical implementation. In the second part of Chapter 3 various ways of decoding cyclic codes are studied and from these considerations, a general decoder for cyclic codes is devised and is presented in Chapter 4. Also, a review of the principal classes of cyclic codes is presented. Chapter 4 describes an experimental system constructed for measuring the performance of cyclic codes initially RC5GI5SCD by random errors and then by bursts of errors. Simulated channels are used both for random and burst errors. A computer simulation of the whole system was made in order to verify the accuracy of the experimental results obtained. Chapter 5 presents the various results obtained with the experimental system and by computer simulation, which allow a comparison of the efficiency of various cyclic codes to be made. Finally, Chapter 6 summarises and dis­cusses the main results of the research and suggests interesting points for future investigation in the area. The main objective of this research is to contribute towards the solution of a fairly wide range of problems arising in the design of efficient coding schemes for practical applications; i.e. a study of coding from an engineering point of view

Coding Theory

Coding theory lies naturally at the intersection of a large number of disciplines in pure and applied mathematics: algebra and number theory, probability theory and statistics, communication theory, discrete mathematics and combinatorics, complexity theory, and statistical physics. The workshop on coding theory covered many facets of the recent research advances

Monitoring system for long-distance pipelines subject to destructive attack

In an era of terrorism, it is important to protect critical pipeline infrastructure, especially in countries where life is strongly dependent on water and the economy on oil and gas. Structural health monitoring (SHM) using acoustic waves is one of the common solutions. However, considerable prior work has shown that pipes are cylindrical acoustic waveguides that support many dispersive, lossy modes; only the torsional T(0, 1) mode has zero dispersion. Although suitable transducers have been developed, these typically excite several modes, and even if they do not, bends and supports induce mode conversion. Moreover, the high-power transducers that could in principle be used to overcome noise and attenuation in long distance pipes present an obvious safety hazard with volatile products, making it difficult to distinguish signals and extract pipeline status information. The problem worsens as the pipe diameter increases or as the frequency rises (due to the increasing number of modes), if the pipe is buried (due to rising attenuation), or if the pipe carries a flowing product (because of additional acoustic noise). Any system is therefore likely to be short-range. This research proposes the use of distributed active sensor network to monitor long-range pipelines, by verifying continuity and sensing small disturbances. A 4-element cuboid Electromagnetic Acoustic Transducer (EMAT) is used to excite the longitudinal L(0,1) mode. Although the EMAT also excites other slower modes, long distance propagation allows their effects to be separated. Correlation detection is exploited to enhance signal-to-noise ratio (SNR), and code division multiplexing access (CDMA) is used to distinguish between nodes in a multi-node system. An extensive numerical search for multiphase quasi-orthogonal codes for different user numbers is conducted. The results suggest that side lobes degrade performance even with the highest possible discrimination factor. Golay complementary pairs (which can eliminate the side lobes completely, albeit at the price of a considerable reduction in speed) are therefore investigated as an alternative. Pipeline systems are first reviewed. Acoustic wave propagation is described using standard theory and a freeware modeling package. EMAT modeling is carried out by numerical calculation of electromagnetic fields. Signal propagation is investigated theoretically using a full system simulator that allows frequency-domain description of transducers, dispersion, multi-mode propagation, mode conversion and multiple reflections. Known codes for multiplexing are constructed using standard algorithms, and novel codes are discovered by an efficient directed search. Propagation of these codes in a dispersive system is simulated. Experiments are carried out using small, unburied air-filled copper pipes in a frequency range where the number of modes is small, and the attenuation and noise are low. Excellent agreement is obtained between theory and experiment. The propagation of pulses and multiplexed codes over distances up to 200 m are successfully demonstrated, and status changes introduced by removable reflectors are detected.Open Acces

Variable Redundancy Coding for Adaptive Error Control

This thesis is concerned with variable redundancy(VR) error control coding. VR coding is proposed as one method of providing efficient adaptive error control for time-varying digital data transmission links. The VR technique involves using a set of short, easy to implement, block codes; rather than the one code of a fixed redundancy system which is usually inefficient, and complex to decode. With a VR system, efficient data-rate low-power codes are used when channel conditions are good, and very high-power inefficient codes are used when the channel is noisy. The decoder decides which code is required to cope with current conditions, and communicates this decision to the encoder by means of a feedback link. This thesis presents a theoretical and practical investigation of the VR technique, and aims to show that when compared with a fixed redundancy system one or more of the advantages of increased average data throughput, decreased maximum probability of erroneous decoding, and decreased complexity can be realised. This is confirmed by the practical results presented in the thesis, which were obtained from field trials of an experimental VR system operating over the HE’ radio channel, and from computer simulations. One consequence of the research has been the inception of a study of codes with disjoint code books and mutual Hamming distance (initially considered for combatting feedback errors), and this topic is introduced in the thesis