Modulated coding for intersymbol interference channels

A study of modulated coding (MC), a technique for intersymbol interference (ISI) mitigation. It discusses MC when the ISI is known at both transmitter and receiver, and when only the receiver knows the ISI. It showcases polynomial antiquity resistant modulated coding, and provides an examination of transmitter-assisted ISI equalization.

Author Notes

Xiang-Gen Xia is an Associate Professor in the Department of Electrical and Computer Engineering, University of Delaware, Newark

K. J. Ray Liu

Series Introduction	p. v
Preface	p. vii
1 Introduction	p. 1
1.1 Post Equalizations	p. 2
1.2 Transmitter Assisted Equalizations	p. 2
1.2.1 TH Precoding	p. 3
1.2.2 Modulated Coding and Vector Coding	p. 4
1.3 Information Rates and Capacity of an ISI Channel with AWGN	p. 5
1.4 Some Notations	p. 7
2 Modulated Codes: Fundamentals and Coding Gain	p. 9
2.1 Modulated Codes	p. 9
2.2 Coding Gain in AWGN Channel	p. 11
2.3 MC Combined with an ISI Channel	p. 13
2.4 Coding Gain in ISI Channels	p. 20
2.5 More Results on Coding Gain	p. 26
2.5.1 Existence of Rate 2/[Gamma] MC with Coding Gain	p. 26
2.5.2 Some Sufficient Conditions on the Existence of Higher Rate Block MC with Coding Gain	p. 33
2.5.3 A Method on the Rate Estimation of MC with Coding Gain	p. 39
2.5.4 Lower and Upper Bounds on the Coding Gain	p. 44
3 Joint Maximum-Likelihood Encoding and Decoding	p. 49
3.1 Performance Analysis of MC	p. 49
3.2 A Method for Computing the Distance Spectrum of Modulated Codes	p. 52
3.2.1 Error-Pattern Trellis	p. 53
3.2.2 Distance Spectrum and Bidirectional Searching Algorithm	p. 57
3.3 Simulation Examples	p. 61
3.4 An Algorithm for Searching the Optimal MC Given an ISI Channel	p. 66
4 Modulated Code Coded Decision Feedback Equalizer	p. 71
4.1 MC Coded Zero-Forcing DFE	p. 71
4.1.1 Performance Analysis	p. 73
4.1.2 The Optimal MC Design	p. 76
4.1.3 Some Simulation Results	p. 78
4.2 MC Coded Minimum Mean Square Error DFE	p. 85
4.2.1 Optimal Decision-Delay and Coefficients of an MC Coded MMSE-DFE	p. 85
4.2.2 Optimal Block MC for MC Coded MMSE-DFE	p. 90
4.2.3 Simulation Results	p. 90
4.3 An Optimal MC Design Converting ISI Channel into ISI-Free Channel	p. 94
4.3.1 An Optimal Modulated Code Design	p. 95
4.3.2 A Sub-optimal Modulated Code Design	p. 98
4.3.3 Delayed Design	p. 102
4.3.4 Some Simulation Results	p. 102
5 Capacity and Information Rates for Modulated Code Coded Intersymbol Interference Channels	p. 111
5.1 Some Lower Bounds of Capacity and Information Rates	p. 112
5.2 MC Existence with Increased Information Rates	p. 114
5.3 Numerical Results	p. 119
5.4 Combined Turbo and MC Coding	p. 122
5.4.1 Joint Turbo and Modulated Code Encoding	p. 123
5.4.2 Joint Soft Turbo and MC Decoding	p. 123
5.4.3 Simulation Results	p. 125
6 Space-Time Modulated Coding for Memory Channels	p. 129
6.1 Channel Model and Space-Time MC	p. 130
6.2 Space-Time MC Coded ZF-DFE	p. 132
6.2.1 MC Coded ZF-DFE and Performance Analysis	p. 132
6.2.2 The Optimal Space-Time MC Design	p. 137
6.3 Capacity and Information Rates of the Space-Time MC Coded MIMO Systems	p. 140
6.3.1 Capacity and Information Rates of MIMO Systems without MC Encoding	p. 140
6.3.2 Capacity and Information Rates of the Space-Time MC Coded MIMO Systems	p. 141
6.4 Numerical Results	p. 148
7 Modulated Code Coded Orthogonal Frequency Division Multiplexing Systems	p. 153
7.1 OFDM Systems for ISI Channels	p. 154
7.2 General MC Coded OFDM Systems for ISI Channels	p. 157
7.3 Channel Independent MC Coded OFDM System for ISI Channels	p. 163
7.3.1 A Special MC	p. 163
7.3.2 An Example	p. 165
7.3.3 Performance Analysis of MC Coded OFDM Systems for ISI Channels	p. 167
7.3.4 Vector OFDM Systems	p. 169
7.3.5 Numerical Results	p. 170
7.4 Channel Independent MC Coded OFDM System for Frequency-Selective Fading Channels	p. 172
7.4.1 Performance Analysis	p. 173
7.4.2 Simulation Results	p. 177
8 Polynomial Ambiguity Resistant Modulated Codes for Blind ISI Mitigation	p. 185
8.1 PARMC: Definitions	p. 187
8.2 Basic Properties and a Family of PARMC	p. 188
8.3 Applications in Blind Identification	p. 194
8.3.1 Blind Identifiability	p. 194
8.3.2 An Algebraic Blind Identification Algorithm	p. 197
8.4 Applications in Communication Systems	p. 200
8.4.1 Applications in Single-Receiver, Baud-Rate Sampled Systems	p. 201
8.4.2 Applications in Undersampled Antenna Array Receiver Systems	p. 203
8.5 Numerical Examples	p. 208
8.5.1 Single Antenna Receiver with Baud Sampling Rate	p. 208
8.5.2 Undersampled Antenna Array Receivers	p. 211
9 Characterization and Construction of Polynomial Ambiguity Resistant Modulated Codes	p. 213
9.1 PAR-Equivalence and Canonical Forms for Irreducible Polynomial Matrices	p. 213
9.2 (Strong) rth PARMC with N ] K	p. 219
9.3 (Strong) rth PARMC with N = K + 1	p. 224
10 An Optimal Polynomial Ambiguity Resistant Modulated Code Design	p. 231
10.1 A Criterion for PARMC Design	p. 231
10.2 Optimal Systematic PARMC	p. 236
10.3 Numerical Examples	p. 238
11 Conclusions and Some Open Problems	p. 243
A Some Fundamentals on Multirate Filterbank Theory	p. 247
A.1 Some Basic Building Blocks	p. 247
A.1.1 Decimator and Expander	p. 248
A.1.2 Noble Identities	p. 249
A.1.3 Polyphase Representations	p. 250
A.2 M-Channel Multirate Filterbanks	p. 251
A.2.1 Maximally Decimated Multirate Filterbanks: Perfect Reconstruction and Aliasing Component Matrix	p. 252
A.2.2 Maximally Decimated Multirate Filterbanks: Perfect Reconstruction and Polyphase Matrix	p. 254
A.3 Perfect Reconstruction FIR Multirate Filterbank Factorization and Construction	p. 257
A.3.1 Factorization of FIR Polyphase Matrices with FIR Inverses	p. 257
A.3.2 Factorization of Paraunitary FIR Matrix Polynomials	p. 260
A.3.3 Perfect Reconstruction Multirate Filterbank Design	p. 262
A.4 DFT and Cosine Modulated Filterbanks	p. 263
A.4.1 DFT Filterbanks	p. 263
A.4.2 Cosine Modulated Filterbanks	p. 265
Bibliography	p. 267
Index	p. 285

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