Turbo Coding

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Springer Science & Business Media, 1999 - Computers - 206 pages
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When the 50th anniversary of the birth of Information Theory was celebrated at the 1998 IEEE International Symposium on Informa tion Theory in Boston, there was a great deal of reflection on the the year 1993 as a critical year. As the years pass and more perspec tive is gained, it is a fairly safe bet that we will view 1993 as the year when the "early years" of error control coding came to an end. This was the year in which Berrou, Glavieux and Thitimajshima pre sented "Near Shannon Limit Error-Correcting Coding and Decoding: Turbo Codes" at the International Conference on Communications in Geneva. In their presentation, Berrou et al. claimed that a combi nation of parallel concatenation and iterative decoding can provide reliable communications at a signal to noise ratio that is within a few tenths of a dB of the Shannon limit. Nearly fifty years of striving to achieve the promise of Shannon's noisy channel coding theorem had come to an end. The implications of this result were immediately apparent to all -coding gains on the order of 10 dB could be used to dramatically extend the range of communication receivers, increase data rates and services, or substantially reduce transmitter power levels. The 1993 ICC paper set in motion several research efforts that have permanently changed the way we look at error control coding.
  

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Contents

Introduction
1
11 Coding Gain
2
12 The Shannon Limit on Performance
5
13 Turbo Coding
6
Bibliography
10
Binary Codes Graphs and Trellises
11
22 Graphs and Trellises
15
23 Labeled Trellises
19
43 Generic Description for Concatenated Codes
78
Bibliography
85
BCE and PCE Performance
89
52 Weight Enumerators and Performance Bounds
96
53 BCE Information Weight Distribution
102
54 PCE Information Weight Distribution
106
55 Summary
117
Bibliography
118

24 Finite State Machines and BCEs
20
241 Minimal Convolutional Encoders
24
242 Systematic Encoders for Convolutional Codes
27
243 The Number of Minimal Encoders
28
25 Trellis Description of a Linear Block Code
29
Bibliography
33
Interleaving
35
31 A Framework for Interleaving
36
32 Block Interleavers
37
321 Classical Block Interleavers
38
33 Multiplex Interleavers
39
331 Classical Convolutional Interleaves
40
341 Decomposition of interleavers
41
342 Interleaver Generator Matrices
42
35 The Shuffle Interleaver
44
36 Interleaver Parameters
47
362 The Memory of an Interleaver
48
363 The Spreading Factors of an Interleaver
50
364 The Dispersion of an Interleaver
52
37 Some Specific Block Interleavers
53
372 WelchCostas Interleaves
54
373 Other Algebraic Interleavers
55
374 PN Random and sRandom Interleavers
58
38 Simulation Results
59
Bibliography
62
Concatenated Codes
65
411 The CCSDS Deep Space Telemetry Standard
66
42 Parallel Concatenated Encoders
77
Turbo Decoding
121
62 Symbol Detection
124
621 Detection by Partitions
126
622 Channels and Sources
130
63 Soft Symbol Detection A DMS over a DMC
133
631 Derivations of Recursions for DMS over DMC
135
632 Soft Symbol Detection FSM Encoder over a DMC
138
64 The Generalized VA and the BCJR
140
641 A Trellis Labeled by a Semiring
141
642 The Generalized Viterbi Algorithm
144
643 The Equivalence of the BCJR and the VA
147
65 Turbo Decoding
149
651 Basic Computation
150
Final Detection Process
156
66 Imperfectly Known Channels
157
Bibliography
162
Belief Propagation and Parallel Decoding
165
71 Reasoning and Probabilistic Networks
166
72 Beliefs and Belief Propagation
173
722 Belief Propagation on Loopy Graphs
179
73 Parallel Turbo Decoding
182
731 The Basic Algorithm
184
74 Variations on a Parallel Theme
188
741 Detailed Descriptions of EP1 and EP2
190
75 Final Thoughts
195
Bibliography
196
Index
199
Copyright

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About the author (1999)

Heegard, Alantro Communications, Inc., CA, and Cornell University, NY, USA.