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Codes and turbo codes

:	Claude Berrou
:	Claude Berrou
:	Codes and turbo codes
:	Springer-Verlag
:	9782817800394
:	1
:	CHF 85.40
:

:	Informatik
:	English

:	400
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

This book is devoted to one of the essential functions of modern telecommunications systems: channel coding or error correction coding. Its main topic is iteratively decoded algebraic codes, convolutional codes and concatenated codes.

	Title Page	3
	Copyright Page	4
	Codes and Turbo Codes	5
	Foreword	7
	Table of Contents	10
	Chapter 1 Introduction	15
	1.1 Digital messages	17
	1.2 A first code	18
	1.3 Hard input decoding and soft input decoding	21
	1.4 Hard output decoding and soft output decoding	25
	1.5 The performance measure	25
	1.6 What is a good code?	29
	1.7 Families of codes	31
	Chapter 2 Digital communications	33
	2.1 DigitalModulations	33
	2.1.1 Introduction	33
	2.1.2 Linear Memoryless Modulations	36
	Amplitude-shift keying with M states: M-ASK	36
	Phase Shift Keying with M states (M-PSK)	39
	Quadrature Amplitude Modulation using two quadrature carriers (MQAM)	40
	2.1.3 Memoryless modulation with M states (M-FSK)	43
	2.1.4 Modulations with memory by continuous phase frequency shift keying (CPFSK)	45
	Continuous phase-frequency-shift keying with modulation index h = 1/2: Minimum Shift Keying (MSK)	46
	L-ary Raised Cosine modulation (L-RC)	48
	Gaussian minimum shift keying modulation (GMSK)	49
	2.2 Structure and performance of the optimal receiver on a Gaussian channel	51
	2.2.1 Structure of the coherent receiver	51
	2.2.2 Performance of the coherent receiver	56
	Amplitude shift keying with M states	56
	Phase shift keying with M states	60
	Amplitude modulation on two quadrature carriers – M-QAM	63
	Frequency shift keying – M-FSK	66
	Continuous phase frequency shift keying – CPFSK	69
	2.3 Transmission on a band-limited channel	73
	2.3.1 Introduction	73
	2.3.2 Intersymbol interference	74
	2.3.3 Condition of absence of ISI: Nyquist criterion	77
	Optimal distribution of filtering between transmission and reception	80
	2.3.4 Expression of the error probability in presence of Nyquist filtering	82
	2.4 Transmission on fading channels	83
	2.4.1 Characterization of a fading channel	83
	Coherence bandwidth	84
	Coherence time	87
	2.4.2 Transmission on non-frequency-selective slow-fading channels	87
	Performance on a Rayleigh channel	87
	Performance on a Rayleigh channel with diversity	89
	Transmission on a slow-fading frequency-selective channel	92
	Transmission with equalization at reception	95
	Chapter 3 Theoretical limits	96
	3.1 Information theory	96
	3.1.1 Transmission channel	96
	3.1.2 An example: the binary symmetric channel	97
	Configurations of errors on the binary symmetric channel	97
	Mutual information and capacity of the binary symmetric channel	98
	3.1.3 Overview of the fundamental coding theorem	99
	3.1.4 Geometrical interpretation	100
	3.1.5 Random coding	101
	Codes imitating random coding	102
	3.2 Theoretical limits to performance	104
	3.2.1 Binary input and real output channel	104
	3.2.2 Capacity of a transmission channel	105
	Shannon limit of a band-limited continuous input and output Gaussian channel	106
	Capacity of a discrete input Gaussian channel	106
	Capacity of the Rayleigh channel	108
	3.3 Practical limits to performance	109
	3.3.1 Gaussian binary input channel	109
	3.3.2 Gaussian continuous input channel	110
	3.3.3 Some examples of limits	112
	3.4 Minimum distances required	113
	3.4.1 MHD required with 4-PSK modulation	113
	3.4.2 MHD required with 8-PSK modulation	115
	3.4.3 MHD required with 16-QAM modulation	117
	Bibliography	120
	Chapter 4 Block codes	121
	4.1 Block codes with binary symbols	122
	4.1.1 Generator matrix of a binary block code	122
	4.1.2 Dual code and parity check matrix	124
	4.1.3 Minimum distance	125
	4.1.4 Extended codes and shortened codes	126
	4.1.5 Product codes	127
	4.1.6 Examples of binary block codes	127
	Parity check code	127
	Repetition code	128
	Hamming code	129
	Maximum length code	130
	Hadamard code	130
	Reed-Muller codes	131
	4.1.7 Cyclic codes	132
	Definition and polynomial representation	132
	Cyclic code in systematic form	134
	Implementation of an encoder	136
	BCH codes	137
	4.2 Block codes with non-binary symbols	142
	4.2.1 Reed-Solomon codes	142
	4.2.2 Implementing the encoder	144
	4.3 Decoding and performance of codes with binary symbols	144
	4.3.1 Error detection	144
	Detection capability	145
	Probability of non-detection of errors	145
	4.3.2 Error correction	146
	Hard decoding	146
	Soft decoding	149
	4.4 Decoding and performance of codes with non-binary symbols . .	155
	4.4.1 Hard input decoding of Reed-Solomon codes	155
	4.4.2 Peterson’s directmethod	156
	Description of the algorithm fo