Advanced Error Control Techniques for Data Storage Systems

Front cover......Page 1
Preface......Page 6
Contributors......Page 8
Contents......Page 10
1.1 Introduction......Page 12
1.2 Linear Codes......Page 14
1.3 Syndrome Decoding, Hamming Codes, and Capacity of the Channel......Page 17
1.4 Codes over Bytes and Finite Fields......Page 19
1.5 Cyclic Codes......Page 21
1.6 Reed Solomon Codes......Page 22
1.7 Decoding of RS Codes: The Key Equation......Page 24
1.8 Decoding RS Codes with Euclid’s Algorithm......Page 27
1.9 Applications: Burst and Random Error Correction......Page 29
2.1 Introduction......Page 34
2.2 Constrained Systems and Codes......Page 35
2.3 Constraints for ISI Channels......Page 37
2.4 Channels with Colored Noise and Intertrack Interference......Page 39
2.5 An Example......Page 40
2.6 Future Directions......Page 42
3.1 Introduction......Page 46
3.2 Asymptotic Information Rate......Page 47
3.3 Other Constraints......Page 49
3.4 Codes for the Noiseless Channel......Page 51
4.1 Introduction......Page 56
4.2 Error Event Characterization......Page 57
4.3 Maximum Transition Run Codes......Page 59
4.4 Detector Design for MTR Constraints......Page 65
4.5 Simulation Results......Page 66
4.6 Summary......Page 67
5.1 Introduction......Page 70
5.3 Dc-free Codes......Page 71
5.4 Codes with Higher Order Spectral Zeros......Page 78
5.5 Composite Constrained and Combined Encoding......Page 84
5.6 Conclusion......Page 87
6.1 Introduction......Page 90
6.2 Bounds......Page 91
6.3 Example: A Trellis Code Construction......Page 93
6.4 An Overview of Some Other Code Constructions......Page 96
6.5 Post Combined Coding System Architectures......Page 100
6.6 Conclusion......Page 101
7.1 Introduction......Page 108
7.2 Configurations......Page 109
7.3 Reverse Concatenation and Soft Iterative Decoding......Page 115
8.1 Introduction......Page 118
8.2 Encoding System Description and Preliminaries......Page 119
8.3 Trellis Codes for Partial-Response Channels Based Upon the Hamming Metric......Page 121
8.4 Trellis-Matched Codes for Partial-Response Channels......Page 124
8.5 Run-Length Limited Trellis-Matched Codes......Page 127
8.6 Avoiding Flawed Codewords......Page 130
Appendix A......Page 132
Appendix B......Page 134
9.1 Introduction......Page 136
9.2 The Channel Model and Capacity Definitions......Page 137
9.3 Trellis Codes, Superchannels and Their Information Rates......Page 141
9.4 Matched Information Rate (MIR) Trellis Codes......Page 144
9.5 Outer LDPC Codes......Page 148
9.6 Optimization Results......Page 151
9.7 Conclusion......Page 154
10.1 Introduction......Page 158
10.3 Multitrack Channel Model......Page 159
10.4 Multitrack Constrained Codes......Page 160
10.5 Multitrack Soft Error-Event Correcting Scheme......Page 162
Turbo Codes......Page 168
11.1 Principles of Turbo Coding......Page 169
11.2 Iterative Decoding of Turbo Codes......Page 173
11.3 Performance of Turbo Codes over AWGN Channels......Page 176
11.4 Recording Channels......Page 178
11.5 Turbo Codes for Recording Channels......Page 179
11.6 Performance of Turbo Codes over Recording Channels......Page 182
11.7 Summary......Page 185
12.1 Introduction......Page 190
12.2 Representations of LPDC Codes......Page 191
12.3 LDPC Code Design Approaches......Page 193
12.4 Iterative Decoding Algorithms......Page 196
12.5 Concluding Remarks......Page 206
13.1 Introduction......Page 210
13.2 System Model......Page 212
13.3 Analysis of Distance Spectrum......Page 214
13.4 Thresholds Analysis using Density Evolution......Page 218
13.5 Simulation Results......Page 222
13.6 Conclusion......Page 225
14.1 Introduction......Page 228
14.2 Combinatorial Designs and their Bipartite Graphs......Page 231
14.3 LDPC Codes on Difference Families......Page 232
14.4 Codes on Projective Planes......Page 234
14.5 Lattice Construction of LDPC Codes......Page 237
14.6 Application in the Partial Response (PR) Channels......Page 239
14.7 Conclusion......Page 243
Turbo Coding for Multitrack Recording Channels......Page 250
15.1 Introduction......Page 251
15.2 Multitrack Recording Channels......Page 252
15.3 Information Theoretical Limits: Achievable Information Rates......Page 254
15.4 Turbo Coding for Multitrack Recording Systems......Page 255
15.5 Discussion......Page 264
Index......Page 268
Back cover......Page 284