Acknowledgments.Historical Perspective, Motivation and Outline. I Convolutional and Block Coding. Convolutional Channel Coding. Block Coding. Soft Decoding and Performance of BCH Codes. II Turbo Convolutional and Turbo Block Coding. Turbo Convolutional Coding. The Super Trellis Structure of Convolutional Turbo Codes. Turbo BCH Coding. Redundant Residue Number System Codes. III Coded Modulation: TCM, TTCM, BICM, BICM ID. Coded Modulation Theory and Performance. IV Space Time Block and Space Time Trellis Coding. Space time Block Codes. Space Time Trellis Codes. Turbo coded Adaptive QAM versus Space time Trellis Coding. V Turbo Equalisation. Turbo coded Partial response Modulation. Turbo Equalisation for Partial response Systems. Turbo Equalisation Performance Bound. Comparative Study of Turbo Equalisers. Reduced complexity Turbo Equaliser. Turbo Equalisation for Space time Trellis coded Systems. Summary and Conclusions. Bibliography. Subject Index. Author Index. About the Authors.Other Related Wiley and IEEE Press Books.

Turbo Coding, Turbo Equalisation and Space-Time Coding for Transmission over Fading Channels

Against the backdrop of the emerging 3G wireless personal communications standards and broadband access network standard proposals, this volume covers a range of coding and transmission aspects for transmission over fading wireless channels. It presents the most important classic channel coding issues and also the exciting advances of the last decade, such as turbo coding, turbo equalisation and space-time coding. It endeavours to be the first book with explicit emphasis on channel coding for transmission over wireless channels. Divided into 4 parts: Part 1 - explains the necessary background for novices. It aims to be both an easy reading text book and a deep research monograph. Part 2 - provides detailed coverage of turbo conventional and turbo block coding considering the known decoding algorithms and their performance over Gaussian as well as narrowband and wideband fading channels. Part 3 - comprehensively discusses both space-time block and space-time trellis coding for the first time in literature. Part 4 - provides an overview of turbo equalisations, also referred to as turbo demodulation. The book systematically converts the lessons of Shannon's information theory into design principles applicable to practical wireless systems. It provides overall design performance studies, giving cognizance to the contradictory design requirements of bit error rate, implementational complexity, coding and interleaving delay, effective throughput, coding rate and other related systems design aspects in a comprehensive manner.

Turbo Coding, Turbo Equalisation and Space-Time Coding

The speed of arithmetic operations depends on the size of the numbers involved. Smaller numbers have faster operations. That is exactly the reason why residue number systems are attractive in computer arithmetic. However, the conversion from residue to binary numbers involves a large number module operations. Several residue-to-binary converters are proposed in this paper. The converters are based on the New Chinese Remainder Theorems (CRT's) I and II which represent our work. The New CRT's improve the celebrated CRT. The new algorithms do not use any large size module adders. The numbers involved are much smaller compared to the numbers in the CRT and its alternative, the Mixed Radix Conversion method. Given a moduli set as (P/sub 1/, P/sub 2/,, P/sub n/), to convert a residue number (x/sub 1/,x/sub 2/,...,x/sub n/) to its decimal correspondence, a matrix of numbers bounded by P/sub i/ is needed for the New CRT I compared to the large numbers M/P/sub i/ for the CRT, where M=P/sub 1/P/sub 2/...P/sub n/. The New CRT II uses module multipliers of size less than /spl radic/M. If the condition P/sub i+1/>P/sub 1/+P/sub 2/+...+P/sub i/ is satisfied, only one module operation of size P/sub n/ is needed for the conversion. Residue-to-binary conversion based on the New CRT's presented here will have a significant impact on many algorithms which currently use the CRT, particularly in computer arithmetic such as residue number systems.

Residue-to-binary converters based on new Chinese remainder theorems

Covering the full range of channel codes from the most conventional through to the most advanced, the second edition of Turbo Coding, Turbo Equalisation and Space-Time Coding is a self-contained reference on channel coding for wireless channels. The book commences with a historical perspective on the topic, which leads to two basic component codes, convolutional and block codes. It then moves on to turbo codes which exploit iterative decoding by using algorithms, such as the Maximum-A-Posteriori (MAP), Log-MAP and Soft Output Viterbi Algorithm (SOVA), comparing their performance. It also compares Trellis Coded Modulation (TCM), Turbo Trellis Coded Modulation (TTCM), Bit-Interleaved Coded Modulation (BICM) and Iterative BICM (BICM-ID) under various channel conditions.The horizon of the content is then extended to incorporate topics which have found their way into diverse standard systems. These include space-time block and trellis codes, as well as other Multiple-Input Multiple-Output (MIMO) schemes and near-instantaneously Adaptive Quadrature Amplitude Modulation (AQAM). The book also elaborates on turbo equalisation by providing a detailed portrayal of recent advances in partial response modulation schemes using diverse channel codes.A radically new aspect for this second edition is the discussion of multi-level coding and sphere-packing schemes, Extrinsic Information Transfer (EXIT) charts, as well as an introduction to the family of Generalized Low Density Parity Check codes.This new edition includes recent advances in near-capacity turbo-transceivers as well as new sections on multi-level coding schemes and of Generalized Low Density Parity Check codesComparatively studies diverse channel coded and turbo detected systems to give all-inclusive information for researchers, engineers and students Details EXIT-chart based irregular transceiver designs Uses rich performance comparisons as well as diverse near-capacity design examples

Turbo Coding, Turbo Equalisation and Space-Time Coding: EXIT-Chart-Aided Near-Capacity Designs for Wireless Channels

Two conversion techniques based on the Chinese remainder theorem are developed for use in residue number systems. The new implementations are fast and simple mainly because adders modulo a large and arbitrary integer M are effectively replaced by binary adders and possibly a lookup table of small address space. Although different in form, both techniques share the same principle that an appropriate representation of the summands must be employed in order to evaluate a sum modulo M efficiently. The first technique reduces the sum modulo M in the conversion formula to a sum modulo 2 through the use of fractional representation, which also exposes the sign bit of numbers. Thus, this technique is particularly useful for sign detection and for any operation requiring a comparison with a binary fraction of M. The other technique is preferable for the full conversion from residues to unsigned or 2's complement integers. By expressing the summands in terms of quotients and remainders with respect to a properly chosen divisor, the second technique systematically replaces the sum modulo M by two binary sums, one accumulating the quotients modulo a power of 2 and the other accumulating the remainders the ordinary way. A final recombination step is required but is easily implemented with a small lookup table and binary adders.

Efficient Implementations of the Chinese Remainder Theorem for Sign Detection and Residue Decoding

In a recent issue of this journal, a hardware implementation of the Chinese Remainder Theorem was proposed for the translation of residue coded outputs into natural integer for an FIR filter realization. The method requires a modulo M adder-shifter network which is not commercially available and has to be constructed from more basic logic elements. This letter presents a more successful technique based on a mixed-radix conversion process. The residue to binary decoder can be built using commercially available elements and requires shorter word lengths in the ROM which stores the output function.

A. Baraniecka

Papers

On decoding techniques for residue number system realizations of digital signal processing hardware