Bernd Friedrichs: Kanalcodierung (in German)

The course "Verfahren zur Kanalcodierung" at the University of Karlsruhe, Germany, is partly based on the textbook (in German):
Bernd Friedrichs: Kanalcodierung - Grundlagen und Anwendungen in modernen Kommunikationssystemen. Unter Mitarbeit von Peter Herbig. Berlin: Springer-Verlag 1995. Reihe Information und Kommunikation (Herausgeber H.Marko und J.Hagenauer).
xv + 508 pages, ISBN 3-540-59353-5.

Price: € 74.95

Parts of the book are available for download:

Vorwort (preface)                     (4 pages, 57 KB)
Inhaltsverzeichnis (contents)   (6 pages, 60 KB)
Kapitel 1 (chapter 1)                (32 pages, 371 KB)

Bernd Friedrichs: Error-Control Coding

Currently I am working on a large extension and revision of the preceeding german book:

Bernd Friedrichs: Error-Control Coding. Berlin: Springer-Verlag. Expected soon.

Some chapters are already available here for download. Note: these are intermediate versions, without final proof-reading, some bookmarks and many cross-references are wrong due to recent changes of chapter and section numbering.

Chapter 1: Introduction to Coded Digital Communications (Coding for Reliable Digital Transmission and Storage; Elements of Digital Communication Systems; Discrete Channel Models; Block Coding; Hamming Distance and Minimum Distance; Maximum-Likelihood Decoding; Asymptotic Coding Gains; The Basic Idea of Error-Correcting Codes)

Chapter 2: Digital Passband Modulation over AWGN Channels (One- and Two-Dimensional AWGN Channels; A Closer Look at the AWGN Channel with Coherent Communication; Some One- and Two-Dimensional Signal Constellations (ASK, PSK, QAM); Performance Analysis of Uncoded Signaling over AWGN Channels; Asymptotic Coding Gains for 2^M-ary Modulation Schemes; Summary of the Most Important Parameters for Coded AWGN Channels)

Chapter 3: Shannon Information Theory (Channel Capacity of Discrete Memoryless Channels; Channel Coding Theorems; Capacity Limits and Coding Gains for the Binary AWGN Channel; C and R_0 for AWGN Channels with High-Level Modulation; Band-Limited AWGN Channels; Appendix: Proof of Shannon's Noisy Channel Coding Theorem for the BSC; Appendix: Proof of the $R_0$ Theorem for the DMC)

Chapter 4: Linear Block Codes (Structure of Linear Block Codes; Error Detection and Correction and Their Geometric Representations; Bounds on Minimum Distance; Asymptotic Bounds on Minimum Distance; The Weight Distribution; Error-Detection Performance; Error-Correction Performance)

Chapter 5: Matrix Description for Linear Block Codes (The Generator Matrix; The Parity-Check Matrix; Dual Codes and MacWilliams Identity; Hamming Codes and Applications; Simple Modifications to a Linear Code; Simple Decoding Techniques)

Chapter 6: Cyclic Block Codes (Polynomial Description of Cyclic Codes; The Generator Polynomial; The Parity-Check Polynomial; Systematic Encoders; The Syndrome Polynomial; Burst-Error and Single-Error Detection Coding; Burst-Error and Single-Error Correction Coding; Non-Algebraic Decoding Techniques)

Chapter 7: The Arithmetic of Galois Fields and Fourier Transforms

Chapter 8: Reed-Solomon and Bose-Chaudhuri-Hocquengham Codes (Representation and Performance of Reed-Solomon Codes; Representation and Performance of Bose-Chaudhuri-Hocquenghem Codes; Decoding Basics: Syndrome and Key Equation; Decoding Architectures; Solving the Key Equation; Error-and-Erasure Decoding with RS Codes; Decoding of Binary BCH Codes; Modifications to RS und BCH Codes)

Chapter 9: Description and Properties of Convolutional Codes (Linear Encoders and Shift Registers; Polynomial Description; Truncated Convolutional Codes; Punctured Convolutional Codes; Further Specific Classes of Convolutional Codes; Catastrophic Codes and Encoder Inverse; Distance Properties and Optimum Convolutional Codes; The Trellis Diagram; State Diagrams and Weight Enumerators)

Chapter 10: Maximum-Likelihood Viterbi Decoding and Performance of Convolutional Codes (Maximum-Likelihood-Decoding and the Viterbi Metric; The Viterbi Algorithm; Calculation of Error Probabilities and Performance Results; Concatenated Codes and Requirements on Soft-Decision Output; The Soft-Output Viterbi Algorithm; Comparison of Block and Convolutional Codes)

Chapter 11: Trellis Coded Modulation

Chapter 12: Concatenated Codes

Chapter 13: Turbo Codes

Chapter 14: More on Specific Codes and Channels (Interleaving Techniques; Fading Channels: Basics and Reed-Solomon Codes; Fading Channels and Trellis Coded Modulation; Channels with Intersymbol Interference and Maximum-Likelihood Sequence Estimation; Continuous Phase Modulation; ML-Decoding of Block Codes with Soft Decisions; Product Codes; Concatenation of Block Codes; Reed-Muller Codes)

Chapter 15: Automatic Repeat Request (ARQ)

Chapter 16: Selected Applications (Satellite Communications; Modems: Data Transmission over the Voice-Band Telephone Channel; The GSM Standard for Mobile Radio; Source and Channel Coding for Future Mobile Radio; Line-of-Sight Microwave Radio; Broadband Wireless Point-to-Multipoint Access Networks; The Compact Disc (CD); Digital Video Broadcasting (DVB); Error-Detection Scheme for ATM)

Appendix: Basic Facts from Algebra and Probability Theory (erster Teil) (Basic Preliminaries; Binomial Coefficients and Entropy Function; Basic Probability Theory; Some important Probability Distributions; The Entropy of a Discrete Random Variable; Algebra (Groups, Rings, Ideals, Fields); Linear Algebra and Vector Spaces; Polynomials; The Extended Version of the Euclidean Algorithm for Polynomials; Polynomial Factor Rings)

Bernd Friedrichs: Ein Beitrag zur Theorie und Anwendung wertdiskreter Adaptionsverfahren in digitalen Empfängern (A contribution to the theory and applications of finite-precision adaptive filters in digital receivers)

Ph.D. thesis, Universität Erlangen-Nürnberg 1990. Ausgewählte Arbeiten über Nachrichtensysteme, Band Nr. 75. Herausgegeben von Prof. Dr.-Ing. W. Schüßler, Lehrstuhl für Nachrichtentechnik, Erlangen.

Preface translated

The focus of this thesis is on adaptive filters as key elements in digital receivers for data communications. Examples include adaptive equalizers or adaptive echo cancelers for full-duplex communication.

Important criteria for the design of digital receivers are generally the implementation complexity as well as the transmission quality measured by the error rate. In case of adaptive filters it is thus essential to achieve a detailed understanding of the relation between the required implementation effort and the impact on the error rate.

Several properties are of considerable importance for the necessary implementation complexity of adaptive filters, this includes the adaptation algorithm (for instance least mean squares algorithm), the length of the filter (given by the number of taps) and the required precision for the digital representation of the variable filter taps. Hence it is essential to consider in detail the finite precision (or quantization) effects for the variable filter and also for the adaptation algorithm.

The implementation complexity of adaptive filters is characterized by the required precision (or wordlength) for the taps. Inaccurate values of the filter coefficients due to limited available precision (due to large quantization steps) can cause considerable degradations of quality. For the exact calculation of the error rate, additional effects have to be analyzed as well, including other impairments or implementation losses of the reeiver as well as transmission noise like co-channel interference.

A two-step approach was adopted for this thesis. In the first part a mathematical analysis for adaptive filters with finite-precision coefficients is presented, focusing on those adaptation algorithms allowing for easy implementations, on the calculation of the residual error floor in steady-state operation and the impact of typical implemention losses. The application of the theoretical results to specific receivers is considered in the second part, in particular the impact of adaptive filters on the transmission quality. Finally, analog-to-digital converters as relevant additional sources of quantization noise are taken into account as well.

Download complete thesis (6050 KB)

The work was performed in context of the development of a commercial ISDN modem.

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