Modern Coding Theory: The Statistical Mechanics and Computer Science Point of View

These are the notes for a set of lectures delivered by the two authors at the Les Houches Summer School on `Complex Systems' in July 2006. They provide an introduction to the basic concepts in modern (probabilistic) coding theory, highlighting connections with statistical mechanics. We also stress common concepts with other disciplines dealing with similar problems that can be generically referred to as `large graphical models'. While most of the lectures are devoted to the classical channel coding problem over simple memoryless channels, we present a discussion of more complex channel models. We conclude with an overview of the main open challenges in the field.Comment: Lectures at Les Houches Summer School on `Complex Systems', July 2006, 44 pages, 25 ps figure

Frequency shift filtering for cyclostationary signals.

The frequency-shift (FRESH) filter is a structure which exploits the spectral correlation of cyclostationary signals for removing interference and noise from a wanted signal. As most digital communication signals are cyclostationary, FRESH filtering offers certain advantages for interference rejection in a communications receiver. This thesis explores the operation and application of FRESH filters in practical interference scenarios. The theoretical background to cyclostationarity is clarified with graphical interpretations of what cyclostationarity is, and how a FRESH filter exploits it to remove interference. The effects of implementation in a sampled system are investigated, in filters which use baud rate related cyclostationarity, leading to efficiency improvements. The effects of varying the wanted signal pulse shape to enhance the cyclostationarity available to the FRESH filter are also investigated. A consistent approach to the interpretation of the FRESH filter's operation is used throughout, while evaluating the performance in a wide range of realistic channel conditions. VLF radio communication is proposed as one area where interference conditions are particularly suitable for the use of FRESH filtering. In cases of severe adjacent channel interference it is found that a FRESH filter can almost completely remove the interferer. The effects of its use with an impulse rejection technique are also investigated. Finally, blind adaptation of FRESH filters through exploitation of carrier related cyclostationarity is investigated. It is found that one existing method loses the advantage of FRESH filtering over time invariant linear filtering. An improvement is proposed to the latter which restores its performance to that of a trained FRESH filter, and also reveals that carrier related cyclostationarity can be exploited, in some cases, by a simpler method. J

Design and analysis of iteratively decodable codes for ISI channels

Recent advancements in iterative processing have allowed communication systems to perform close to capacity limits withmanageable complexity.For manychannels such as the AWGN and flat fading channels, codes that perform only a fraction of a dB from the capacity have been designed in the literature. In this dissertation, we will focus on the design and analysis of near-capacity achieving codes for another important class of channels, namely inter-symbol interference (ISI)channels. We propose various coding schemes such as low-density parity-check (LDPC) codes, parallel and serial concatenations for ISI channels when there is no spectral shaping used at the transmitter. The design and analysis techniques use the idea of extrinsic information transfer (EXIT) function matching and provide insights into the performance of different codes and receiver structures. We then present a coding scheme which is the concatenation of an LDPC code with a spectral shaping block code designed to be matched to the channel??s spectrum. We will discuss how to design the shaping code and the outer LDPC code. We will show that spectral shaping matched codes can be used for the parallel concatenation to achieve near capacity performance. We will also discuss the capacity of multiple antenna ISI channels. We study the effects of transmitter and receiver diversities and noisy channel state information on channel capacity

Channel Coding in Molecular Communication

This dissertation establishes and analyzes a complete molecular transmission system from a communication engineering perspective. Its focus is on diffusion-based molecular communication in an unbounded three-dimensional fluid medium. As a basis for the investigation of transmission algorithms, an equivalent discrete-time channel model (EDTCM) is developed and the characterization of the channel is described by an analytical derivation, a random walk based simulation, a trained artificial neural network (ANN), and a proof of concept testbed setup. The investigated transmission algorithms cover modulation schemes at the transmitter side, as well as channel equalizers and detectors at the receiver side. In addition to the evaluation of state-of-the-art techniques and the introduction of orthogonal frequency-division multiplexing (OFDM), the novel variable concentration shift keying (VCSK) modulation adapted to the diffusion-based transmission channel, the lowcomplex adaptive threshold detector (ATD) working without explicit channel knowledge, the low-complex soft-output piecewise linear detector (PLD), and the optimal a posteriori probability (APP) detector are of particular importance and treated. To improve the error-prone information transmission, block codes, convolutional codes, line codes, spreading codes and spatial codes are investigated. The analysis is carried out under various approaches of normalization and gains or losses compared to the uncoded transmission are highlighted. In addition to state-of-the-art forward error correction (FEC) codes, novel line codes adapted to the error statistics of the diffusion-based channel are proposed. Moreover, the turbo principle is introduced into the field of molecular communication, where extrinsic information is exchanged iteratively between detector and decoder. By means of an extrinsic information transfer (EXIT) chart analysis, the potential of the iterative processing is shown and the communication channel capacity is computed, which represents the theoretical performance limit for the system under investigation. In addition, the construction of an irregular convolutional code (IRCC) using the EXIT chart is presented and its performance capability is demonstrated. For the evaluation of all considered transmission algorithms the bit error rate (BER) performance is chosen. The BER is determined by means of Monte Carlo simulations and for some algorithms by theoretical derivation

A unified approach to the analysis and design of digital line codes

In most areas of research the variety of possible approaches to analysis and design problems is very large. This is particularly true in the case of digital signal transmission where various conflicting requirements exist (e.g. minimum bandwidth for maximum information capacity and reliability). The lack of universally adopted analysis and evaluation methods is not due to any uncertainties or deficiencies in theoretical fundamentals, rather it is a problem of diversity of criteria and therefore modes of specification that apply. The work presented in the thesis is concerned with the creation and evaluation of a universal algorithm suitable for the assessment of digital codes together with a systematic approach to the comparative evaluation of essential structural and spectral features of coding schemes. The thesis begins with an overview of the basic theoretical principles of line coding as an essential part of the process of channel coding for reliable and efficient digital signal transmission. A general spectral analysis procedure is derived from the finite-state sequential machine model of fixed-length block coders, and is implemented in the form of a computer program. A technique for the conversion of coder rules, given in descriptive form into table and matrix form, suitable for the universal specification format used in the general spectral analysis procedure, is developed. A new method of general classification of codes into categories, according to their complexity levels, is proposed. A modification of the spectral analysis routine into a universal block-code generating scheme is then introduced. The virtually unlimited capabilities for the design and analysis of new code structures is demonstrated. Following from this, a new method for evaluation of the performance of block codes is suggested. It is based on the introduction of an integral parameter, the Information Capacity, which determines the degree of possible spectrum modification for a particular coder specification. Using this method, it is demonstrated how an optimal combination of a code structure, spectral features and information capacity can be achieved. The thesis concludes with a practical example of the application of the generalised analysis procedure, demonstrating the possibility to combine code multiplexing with modification of the spectrum of the line signal. A novel technique, based on the principles of spread spectrum for multichannel transmission, is proposed. It involves a Binary-Multiplexed Coding (BMC) scheme which is implemented in a generalised circuit, the performance of which is investigated and evaluated

Blind channel identification/equalization with applications in wireless communications

Ph.DDOCTOR OF PHILOSOPH

EXIT charts for system design and analysis

Near-capacity performance may be achieved with the aid of iterative decoding, where extrinsic soft information is exchanged between the constituent decoders in order to improve the attainable system performance. Extrinsic information Transfer (EXIT) charts constitute a powerful semi-analytical tool used for analysing and designing iteratively decoded systems. In this tutorial, we commence by providing a rudimentary overview of the iterative decoding principle and the concept of soft information exchange. We then elaborate on the concept of EXIT charts using three iteratively decoded prototype systems as design examples. We conclude by illustrating further applications of EXIT charts, including near-capacity designs, the concept of irregular codes and the design of modulation schemes