Fundamentals of Convolutional Coding.
- 2nd ed.
- 1 online resource (689 pages)
- IEEE Series on Digital and Mobile Communication Series .
- IEEE Series on Digital and Mobile Communication Series .
Intro -- FUNDAMENTALS OF CONVOLUTIONAL CODING -- Contents -- Preface -- Acknowledgement -- 1 Introduction -- 1.1 Why error control? -- 1.2 Block codes-a primer -- 1.3 Codes on graphs -- 1.4 A first encounter with convolutional codes -- 1.5 Block codes versus convolutional codes -- 1.6 Capacity limits and potential coding gain revisited -- 1.7 Comments -- Problems -- 2 Convolutional encoders-Structural properties -- 2.1 Convolutional codes and their encoders -- 2.2 The Smith form of polynomial convolutional generator matrices -- 2.3 Encoder inverses -- 2.4 Encoder and code equivalences -- 2.5 Basic encoding matrices -- 2.6 Minimalbasic encoding matrices -- 2.7 Minimal encoding matrices and minimal encoders -- 2.8 Canonical encoding matrices* -- 2.9 Minimality via the invariantfactor theorem* -- 2.10 Syndrome formers and dual encoders -- 2.11 Systematic convolutional encoders -- 2.12 Some properties of generator matrices-an overview -- 2.13 Comments -- Problems -- 3 Distance properties of convolutional codes -- 3.1 Distance measures-a first encounter -- 3.2 Active distances -- 3.3 Properties of convolutional codes via the active distances -- 3.4 Lower bound on the distance profile -- 3.5 Upper bounds on the free distance -- 3.6 Timevarying convolutional codes -- 3.7 Lower bound on the free distance -- 3.8 Lower bounds on the active distances* -- 3.9 Distances of cascaded concatenated codes* -- 3.10 Path enumerators -- 3.11 Comments -- Problems -- 4 Decoding of convolutional codes -- 4.1 The Viterbi algorithm revisited -- 4.2 Error bounds for timeinvariant convolutional codes -- 4.3 Tighter error bounds for timeinvariant convolutional codes -- 4.4 Exact bit error probability for Viterbi decoding -- 4.5 The BCJR algorithm for APP decoding -- 4.6 The oneway algorithm for APP decoding. 4.7 A simple upper bound on the bit error probability for extremely noisy channels -- 4.8 Tailbiting trellises -- 4.9 Decoding of tailbiting codes -- 4.10 BEAST decoding of tailbiting codes -- 4.11 Comments -- Problems -- 5 Random ensemble bounds for decoding error probability -- 5.1 Upper bounds on the output error burst lengths -- 5.2 Bounds for periodically timevarying convolutional codes -- 5.3 Lower error probability bounds for convolutional codes -- 5.4 General bounds for timevarying convolutional codes -- 5.5 Bounds for finite backsearch limits -- 5.6 Quantization of channel outputs -- 5.7 Comments -- Problems -- 6 List decoding -- 6.1 List decoding algorithms -- 6.2 List decoding-performance -- 6.3 The list minimum weight -- 6.4 Upper bounds on the probability of correct path loss -- 6.5 Lower bound on the probability of correct path loss -- 6.6 Correct path loss for timeinvariant convolutional codes -- 6.7 Comments -- Problems -- 7 Sequential decoding -- 7.1 The Fano metric -- 7.2 The stack algorithm -- 7.3 The Fano algorithm -- 7.4 The Creeper algorithm* -- 7.5 Simulations -- 7.6 Computational analysis of the stack algorithm -- 7.7 Error probability analysis of the stack algorithm -- 7.8 Analysis of the Fano algorithm -- 7.9 Analysis of Creeper* -- 7.10 Comments -- Problems -- 8 Lowdensity paritycheck codes -- 8.1 LDPC block codes -- 8.2 LDPC convolutional codes -- 8.3 Block and convolutional permutors -- 8.4 Lower bounds on distances of LDPC codes -- 8.5 Iterative decoding of LDPC codes -- 8.6 Iterative limits and thresholds -- 8.7 Braided block codes* -- 8.8 Comments -- Problems -- 9 Turbo coding -- 9.1 Parallel concatenation of two convolutional codes -- 9.2 Distance bounds of turbo codes -- 9.3 Parallel concatenation of three and more convolution codes -- 9.4 Iterative decoding of turbo codes -- 9.5 Braided convolutional codes*. 9.6 Comments -- Problems -- 10 Convolutional codes with good distance properties -- 10.1 Computing the Viterbi spectrum using FAST -- 10.2 The magnificient BEAST -- 10.3 Some classes of rate R = 1=2 convolutional codes -- 10.4 Low rate convolutional codes -- 10.5 High rate convolutional codes -- 10.6 Tailbiting trellis encoders -- 10.7 Comments -- Appendix A: Minimal encoders -- Appendix B: Wald's identity -- References -- Index -- EULA.