Codes for Digital Recorders

Constrained codes are a key component in digital recording devices that have become ubiquitous in computer data storage and electronic entertainment applications. This paper surveys the theory and practice of constrained coding, tracing the evolution of the subject from its origins in Shannon's classic 1948 paper to present-day applications in high-density digital recorders. Open problems and future research directions are also addressed.

[1]  Peter A. Franaszek,et al.  A DC-Balanced, Partitioned-Block, 8B/10B Transmission Code , 1983, IBM J. Res. Dev..

[2]  Shu Lin,et al.  Error control coding : fundamentals and applications , 1983 .

[3]  Emina Soljanin,et al.  Multihead Detection for Multitrack Recording Channels , 1998, IEEE Trans. Inf. Theory.

[4]  K.A.S. Immink,et al.  On the construction of constrained codes employing sequence replacement techniques , 1997, Proceedings of IEEE International Symposium on Information Theory.

[5]  Noga Alon,et al.  Balancing sets of vectors , 1988, IEEE Trans. Inf. Theory.

[6]  R. T. Behrens,et al.  An advanced read/write channel for magnetic disk storage , 1992, [1992] Conference Record of the Twenty-Sixth Asilomar Conference on Signals, Systems & Computers.

[7]  Hisashi Kobayashi,et al.  A Survey of Coding Schemes for Transmission or Recording of Digital Data , 1971 .

[8]  K.A.S. Immink,et al.  Weakly constrained codes , 1997 .

[9]  Jack K. Wolf,et al.  Trellis codes for (1,k) E/sup 2/PR4ML with squared distance 18 , 1996 .

[10]  P. Funk,et al.  Run-length-limited codes with multiple spacing , 1982 .

[11]  A. Wijngaarden,et al.  SIMPLE HIGH-RATE CONSTRAINED CODES , 1996 .

[12]  H. Freeman Calculation of Mean Shift for a Binary Multiplier Using 2, 3, or 4 Bits at a Time , 1967, IEEE Trans. Electron. Comput..

[13]  S. Shantai,et al.  Information Rates For A Discrete-time Gaussian Channel With Intersymbol Interference And Stationary Inputs , 1991, Proceedings. 1991 IEEE International Symposium on Information Theory.

[14]  Kees A. Schouhamer Immink,et al.  Runlength-limited sequences , 1990, Proc. IEEE.

[15]  Emina Soljanin,et al.  An interleaved coding scheme for (1-D)(1+D)/sup 2/ partial response with concatenated decoding , 1996, Proceedings of GLOBECOM'96. 1996 IEEE Global Telecommunications Conference.

[16]  H. Neal Bertram,et al.  Theory of Magnetic Recording , 1994 .

[17]  L. Rothschild,et al.  The distribution of English dictionary word lengths , 1986 .

[18]  J D Ullman,et al.  Finite-state Modulation Codes for Data Storage, Ieee Sliding-block Coding for Input-restricted Channels, Ieee , .

[19]  Brian H. Marcus,et al.  Finite-State Modulation Codes for Data Storage , 2004 .

[20]  Peter A. Franaszek A General Method for Channel Coding , 1980, IBM J. Res. Dev..

[21]  Aaron D. Wyner,et al.  Achievable rates for a constrained Gaussian channel , 1988, IEEE Trans. Inf. Theory.

[22]  P. A. Franasnek On future-dependent block coding for input-restricted channels , 1979 .

[23]  Joel G. Smith,et al.  The Information Capacity of Amplitude- and Variance-Constrained Scalar Gaussian Channels , 1971, Inf. Control..

[24]  Kenneth J. Kerpez,et al.  The power spectral density of maximum entropy charge constrained sequences , 1989, IEEE Trans. Inf. Theory.

[25]  Ron M. Roth,et al.  Bounds On The Number Of States In Encoder Graphs For Input-constrained Channels , 1991, Proceedings. 1991 IEEE International Symposium on Information Theory.

[26]  Hirofumi Yoshida,et al.  8–9 Block Code: A DC-Free Channel Code for Digital Magnetic Recording , 1983 .

[27]  Paul H. Siegel,et al.  Distance-enhancing codes for digital recording , 1998 .

[28]  Paul H. Siegel,et al.  Recording codes for digital magnetic storage , 1985 .

[29]  Lambertus Hesselink,et al.  Channel codes for digital holographic data storage , 1995 .

[30]  E. Kretzmer,et al.  Generalization of a Techinque for Binary Data Communication , 1966 .

[31]  Henk D. L. Hollmann Bounded-delay-encodable, block-decodable codes for constrained systems , 1996, IEEE Trans. Inf. Theory.

[32]  A. Robert Calderbank,et al.  Binary convolutional codes with application to magnetic recording , 1986, IEEE Trans. Inf. Theory.

[33]  J. Wolf,et al.  Bit-stuffing bounds on the capacity of 2-dimensional constrained arrays , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[34]  S C Esener,et al.  Partial response precoding for parallel readout optical memories , 1993, Optics & Photonics.

[35]  S. Takahashi,et al.  Digital modulation method for recordable digital video disc , 1996, 1996. Digest of Technical Papers., International Conference on Consumer Electronics.

[36]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[37]  Roy D. Cideciyan,et al.  A PRML System for Digital Magnetic Recording , 1992, IEEE J. Sel. Areas Commun..

[38]  Thomas M. Cover,et al.  Enumerative source encoding , 1973, IEEE Trans. Inf. Theory.

[39]  A. Robert Calderbank,et al.  Coset codes for partial response channels; or, coset codes with spectral nulls , 1989, IEEE Trans. Inf. Theory.

[40]  A. Vardy,et al.  High-order spectral-null codes: constructions and bounds , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[41]  Abraham Lempel,et al.  Look-ahead coding for input- restricted channels , 1982, IEEE Trans. Inf. Theory.

[42]  Kees A. Schouhamer Immink,et al.  A generalized method for encoding and decoding run-length-limited binary sequences , 1983, IEEE Trans. Inf. Theory.

[43]  G. David Forney,et al.  Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference , 1972, IEEE Trans. Inf. Theory.

[44]  Hisashi Kobayashi,et al.  Application of partial-response channel coding to magnetic recording systems , 1970 .

[45]  Brian H. Marcus,et al.  On codes with spectral nulls at rational submultiples of the symbol frequency , 1987, IEEE Trans. Inf. Theory.

[46]  Robert H. Deng,et al.  DC-free coset codes , 1988, IEEE Trans. Inf. Theory.

[47]  Paul H. Siegel,et al.  Complexity and sliding-block decodability , 1996, IEEE Trans. Inf. Theory.

[48]  Roger W. Wood,et al.  Viterbi Detection of Class IV Partial Response on a Magnetic Recording Channel , 1986, IEEE Trans. Commun..

[49]  Stephen B. Wicker,et al.  Applications of Error-Control Coding , 1998, IEEE Trans. Inf. Theory.

[50]  Paul H. Siegel,et al.  The power spectrum of run-length-limited codes , 1989, IEEE Trans. Commun..

[51]  A. Robert Calderbank,et al.  A Modified Concatenated Coding Scheme, with Applications to Magnetic Data Storage , 1998, IEEE Trans. Inf. Theory.

[52]  Kees A. Schouhamer Immink,et al.  Performance assessment of dc-free multimode codes , 1997, IEEE Trans. Commun..

[53]  Necip Sayiner Impact of the track density versus linear density trade-off on the read channel: TCPR4 versus EPR4 , 1995, Other Conferences.

[54]  Paul H. Siegel,et al.  Conservative arrays: multidimensional modulation codes for holographic recording , 1996, IEEE Trans. Inf. Theory.

[55]  Kees A. Schouhamer Immink,et al.  Entropy and power spectrum of asymmetrically DC-constrained binary sequences , 1991, IEEE Trans. Inf. Theory.

[56]  Peter A. Franaszek,et al.  Coding for Constrained Channels: A Comparison of Two Approaches , 1989, IBM J. Res. Dev..

[57]  Jack K. Wolf,et al.  Finite truncation depth trellis codes for the dicode channel , 1995 .

[58]  R. Kost,et al.  Binary two-thirds rate code with full word look-ahead , 1984 .

[59]  Kornelis Antonie Immink Block-Decodable Runlength-Limited Codes via Look-Ahead Technique , 1993, Proceedings. IEEE International Symposium on Information Theory.

[60]  J. Wolf,et al.  A new class of two-dimensional RLL recording codes , 1992 .

[61]  J. Pierce,et al.  Spectra and Efficiency of Binary Codes Without DC , 1972, IEEE Trans. Commun..

[62]  V. Braun,et al.  On the low-frequency suppression performance of DC-free runlength-limited modulation codes , 1996 .

[63]  M. Cohn,et al.  Run-length reduction of 3PM code via look-ahead technique , 1982 .

[64]  L Hesselink,et al.  Volume Holographic Storage and Retrieval of Digital Data , 1994, Science.

[65]  B. Marcus Constrained Systems and Coding for Recording Channels, in Handbook of Coding Theory, v. Finite-state Modulation Codes for Data Storage, Ieee , 2000 .

[66]  Heitaro Nakajima,et al.  A Rotary Head High Density Digital Audio Tape Recorder , 1983, IEEE Transactions on Consumer Electronics.

[67]  Kees Schouhamer-Immink Coding Techniques for Digital Recorders , 1991 .

[68]  D. A. Bell,et al.  Information Theory and Reliable Communication , 1969 .

[69]  E.R. Berlekamp,et al.  The technology of error-correcting codes , 1980, Proceedings of the IEEE.

[70]  Susumu Yoshida,et al.  On the Relation between an Encoding Automaton and the Power Spectrum of Its Output Sequence , 1976 .

[71]  Peter Kabal,et al.  Partial-Response Signaling , 1975, IEEE Trans. Commun..

[72]  Michael W. Marcellin,et al.  Two-dimensional Modulation Codes , 1991, Proceedings. 1991 IEEE International Symposium on Information Theory.

[73]  Ivan J. Fair,et al.  Guided scrambling: a new line coding technique for high bit rate fiber optic transmission systems , 1991, IEEE Trans. Commun..

[74]  M. Hassner,et al.  Algorithms for sliding block codes - An application of symbolic dynamics to information theory , 1983, IEEE Trans. Inf. Theory.

[75]  Jack K. Wolf,et al.  On saving decoder states for some trellis codes and partial response channels , 1988, IEEE Trans. Commun..

[76]  Hisashi Kobayashi,et al.  Correlative level coding and maximum-likelihood decoding , 1971, IEEE Trans. Inf. Theory.

[77]  Tuvi Etzion,et al.  Cascading methods for runlength-limited arrays , 1997, IEEE Trans. Inf. Theory.

[78]  P. A. Franaszek,et al.  Sequence-state coding for digital transmission , 1968 .

[79]  T. Etzion,et al.  Efficient code constructions for certain two-dimensional constraints , 1997, Proceedings of IEEE International Symposium on Information Theory.

[80]  Kees A. Schouhamer Immink Constructions of almost block-decodable runlength-limited codes , 1995, IEEE Trans. Inf. Theory.

[81]  Khaled A. S. Abdel-Ghaffar,et al.  Constrained block codes for class-IV partial-response channels with maximum-likelihood sequence estimation , 1996, IEEE Trans. Inf. Theory.

[82]  S Hunter,et al.  Potentials of two-photon based 3-D optical memories for high performance computing. , 1990, Applied optics.

[83]  Walter Hirt Capacity and information rates of discrete-time channels with memory , 1988 .

[84]  Kees A. Schouhamer Immink,et al.  Binary transmission codes with higher order spectral zeros at zero frequency , 1987, IEEE Trans. Inf. Theory.

[85]  A. Robert Calderbank,et al.  Coded modulation and precoding for electron-trapping optical memories , 1998, IEEE Trans. Commun..

[86]  M. Ferguson Optimal reception for binary partial response channels , 1972 .

[87]  Brian H. Marcus,et al.  Sliding-block coding for input-restricted channels , 1988, IEEE Trans. Inf. Theory.

[88]  W T Welford,et al.  Principles of Optical Disc Systems , 1986 .

[89]  Gianfranco L. Pierobon,et al.  Codes for zero spectral density at zero frequency , 1984, IEEE Trans. Inf. Theory.

[90]  Roger Wood,et al.  Denser magnetic memory , 1990 .

[91]  On the capacity of two dimensional run length limited codes , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[92]  William F. Coscarelli,et al.  The Compact Disc Handbook , 1994 .

[93]  Brian Marcus Symbolic dynamics and coding applications , 1995, Proceedings of 1995 IEEE International Symposium on Information Theory.

[94]  R. Wood Magnetic megabits , 1990, IEEE Spectrum.

[95]  William H. Kautz Ieee Transactions on Information Theory Co~tcluding Remarks , 2022 .

[96]  Donald E. Knuth,et al.  Efficient balanced codes , 1986, IEEE Trans. Inf. Theory.

[97]  J. C. Mallinson,et al.  Optimal codes for digital magnetic recording , 1977 .

[98]  Paul H. Siegel,et al.  Error-Event Characterization on Partial-Response Channels , 1999, IEEE Trans. Inf. Theory.

[99]  Jack K. Wolf,et al.  Trellis Coding for Partial-Response Channels , 1986, IEEE Trans. Commun..

[100]  Paul H. Siegel,et al.  Matched spectral-null codes for partial-response channels , 1989, IEEE Trans. Inf. Theory.

[101]  Tjalling J. Tjalkens On the principal state method for run-length limited sequences , 1994, IEEE Trans. Inf. Theory.

[102]  V. Braun,et al.  On the application of sequence estimation algorithms in the digital compact cassette (DCC) , 1994 .

[103]  B. Brickner,et al.  Design Of a Rate 5/6 Maximum Transition Run Code , 1997, 1997 IEEE International Magnetics Conference (INTERMAG'97).

[104]  Chris Heegard,et al.  Bounding the Capacity of Saturation Recording: The Lorentz Model and Applications , 1992, IEEE J. Sel. Areas Commun..

[105]  Kees A. Immink Modulation systems for digital audio discs with optical readout , 1981, ICASSP.

[106]  G. Jacoby A new look-ahead code for increased data density , 1977 .

[107]  Brian H. Marcus,et al.  Sofic systems and encoding data , 1985, IEEE Trans. Inf. Theory.

[108]  H. Thapar,et al.  A class of partial response systems for increasing storage density in magnetic recording , 1987 .

[109]  Y. Shimpuku,et al.  8/10 modulation codes for digital magnetic recording , 1986 .

[110]  N. Ohta,et al.  MAGNETIC MULTI-VALJUED MAGNETO-OPTICAL DISK , 1995 .

[111]  J. Wolf,et al.  BINARY TO TERNARY CONVERSION BY LINEAR FILTERING , 1962 .

[112]  L Hesselink,et al.  Signal detection for page-accessoptical memories with intersymbol interference. , 1996, Applied optics.

[113]  Kees A. Schouhamer Immink The Digital Versatile Disc (DVD): System Requirements and Channel Coding , 1996 .

[114]  Paul H. Siegel,et al.  Recording Results And Coding Considerations For The Resonant Bias Coil Overwrite Technique , 1989, Photonics West - Lasers and Applications in Science and Engineering.

[115]  Ephraim Zehavi,et al.  CODING FOR MAGNETIC RECORDING , 1987 .

[116]  Steven W. McLaughlin,et al.  Five runlength-limited codes for M-ary recording channels , 1997 .

[117]  D. Bloomberg,et al.  Channel capacity of charge-constrained run-length limited codes , 1981 .

[118]  Shlomo Shamai,et al.  Information rates for magnetic recording channels with peak- and slope-limited magnetization , 1989, IEEE Trans. Inf. Theory.

[119]  B. Marcus Symbolic Dynamics and Connections to Coding Theory, Automata Theory and System Theory , 1995 .

[120]  W. Bliss,et al.  An 8/9 Rate Time-varying Trellis Code For High Density Magnetic Recording , 1997, 1997 IEEE International Magnetics Conference (INTERMAG'97).

[121]  Evangelos Eleftheriou,et al.  On codes satisfying M th-order running digital sum constraints , 1991, IEEE Trans. Inf. Theory.

[122]  James L. Massey,et al.  Capacity of the discrete-time Gaussian channel with intersymbol interference , 1988, IEEE Trans. Inf. Theory.

[123]  Paul H. Siegel,et al.  Design and performance of a VLSI 120 Mb/s trellis-coded partial response channel , 1995 .

[124]  Henk D. L. Hollmann On the construction of bounded-delay encodable codes for constrained systems , 1995, IEEE Trans. Inf. Theory.

[125]  Jack K. Wolf,et al.  A new rate 2/3 sliding block code for the (1, 7) runlength constraint with the minimal number of encoder states , 1991, IEEE Trans. Inf. Theory.

[126]  Emina Soljanin On-track and off-track distance properties of Class 4 partial response channels , 1995, Other Conferences.

[127]  J. Watkinson Editing in RDAT , 1990 .

[128]  J.K. Wolf,et al.  Distance Spectra For PRML Channels , 1997, 1997 IEEE International Magnetics Conference (INTERMAG'97).

[129]  Yinyi Lin,et al.  Modulation codes , 1997 .

[130]  Paul H. Siegel,et al.  Improved Trellis-coding For Partial Response Channels , 1994, Digest of the Magnetic Recording Conference.

[131]  Jian Gu,et al.  A new approach to constructing optimal block codes for runlength-limited channels , 1994, IEEE Trans. Inf. Theory.

[132]  John M. Cioffi,et al.  Sliding-Block Line Codes to Increase Dispersion-Limited Distance of Optical Fiber Channels , 1995, IEEE J. Sel. Areas Commun..

[133]  J. Watkinson The art of digital audio , 1988 .

[134]  Paul H. Siegel,et al.  Coding for higher-order partial-response channels , 1995, Other Conferences.

[135]  Peter A. Franaszek Synchronous Bounded Delay Coding for Input Restricted Channels , 1980, IBM J. Res. Dev..

[136]  Ta-Mu Chien,et al.  Upper bound on the efficiency of dc-constrained codes , 1970, Bell Syst. Tech. J..

[137]  Kjell Jørgen Hole Punctured convolutional codes for the 1-D partial-response channel , 1991, IEEE Trans. Inf. Theory.

[138]  K.A.S. Immink Spectral null codes , 1990 .

[139]  M. Berkoff,et al.  Waveform compression in NRZI magnetic recording , 1964 .

[140]  K. Knudson Fitzpatrick,et al.  Time-varying MTR codes for high density magnetic recording , 1997, GLOBECOM 97. IEEE Global Telecommunications Conference. Conference Record.

[141]  Arvind M. Patel Zero-modulation encoding in magnetic recording , 1975 .

[142]  Brian H. Marcus,et al.  Construction of encoders with small decoding look-ahead for input-constrained channels , 1995, IEEE Trans. Inf. Theory.

[143]  Carlo M. Monti,et al.  Codes with a multiple spectral null at zero frequency , 1989, IEEE Trans. Inf. Theory.

[144]  Paul H. Siegel,et al.  Constrained coding for binary channels with high intersymbol interference , 1999, IEEE Trans. Inf. Theory.

[145]  K. W. Cattermole Invited paper Principles of digital line coding , 1983 .

[146]  Jørn Justesen,et al.  Information rates and power spectra of digital codes , 1982, IEEE Trans. Inf. Theory.

[147]  R. Blahut,et al.  The capacity and coding gain of certain checkerboard codes , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[148]  Aaron D. Wyner,et al.  Optimum Block Codes for Noiseless Input Restricted Channels , 1964, Inf. Control..

[149]  Jaekyun Moon,et al.  Maximum transition run codes for data storage systems , 1996 .

[150]  Hisashi Kobayashi,et al.  Application of probabilistic decoding to digital magnetic recording systems , 1971 .

[151]  Jack K. Wolf,et al.  New model for media noise in thin-film magnetic recording media , 1995, Other Conferences.

[152]  Jaekyun Moon,et al.  Design of a rate 6/7 maximum transition run code , 1997 .

[153]  Kees A. Schouhamer Immink A practical method for approaching the channel capacity of constrained channels , 1997, IEEE Trans. Inf. Theory.

[154]  Brian H. Marcus,et al.  Canonical Encoders for Sliding Block Decoders , 1995, SIAM J. Discret. Math..

[155]  Peter A. Franaszek Construction of Bounded Delay Codes for Discrete Noiseless Channels , 1982, IBM J. Res. Dev..

[156]  Ken C. Pohlman The compact disc handbook (2nd ed.) , 1992 .

[157]  William G. Bliss,et al.  The performance of generalized maximum transition run trellis codes , 1998 .

[158]  Brian H. Marcus,et al.  A generalized state-splitting algorithm , 1997, IEEE Trans. Inf. Theory.

[159]  Kjell Jørgen Hole,et al.  Improved coding techniques for preceded partial-response channels , 1994, IEEE Trans. Inf. Theory.

[160]  Jack K. Wolf,et al.  Bounds on the capacity of a peak power constrained Gaussian channel , 1988 .

[161]  Lalit R. Bahl,et al.  Block Codes for a Class of Constrained Noiseless Channels , 1970, Inf. Control..

[162]  P. Franaszek Sequence-state methods for run-length-limited coding , 1970 .

[163]  R. L. Adler,et al.  The torus and the disk , 1987 .

[164]  L.C. Barbosa Simultaneous detection of readback signals from interfering magnetic recording tracks using array heads , 1990, International Conference on Magnetics.

[165]  Jack K. Wolf,et al.  Applications of a new simulation model for media noise limited magnetic recording channels , 1996 .

[166]  K. W. Cattermole,et al.  Principles of pulse code modulation , 1969 .

[167]  P.H. Siegel,et al.  Modulation and coding for information storage , 1991, IEEE Communications Magazine.

[168]  Shlomo Shamai,et al.  Upper bounds on capacity for a constrained Gaussian channel , 1989, IEEE Trans. Inf. Theory.

[169]  Andrew Gabor,et al.  Adaptive Coding for Self-Clocking Recording , 1967, IEEE Trans. Electron. Comput..

[170]  Brian H. Marcus,et al.  Two-dimensional low-pass filtering codes , 1998, IEEE Trans. Commun..

[171]  Hiroshi Kamabe,et al.  Minimum scope for sliding block decoder mappings , 1989, IEEE Trans. Inf. Theory.

[172]  G. David Forney,et al.  Modulation and Coding for Linear Gaussian Channels , 1998, IEEE Trans. Inf. Theory.

[173]  Kees A. Schouhamer Immink,et al.  Channel code with embedded pilot tracking tones for DVCR , 1995 .

[174]  Laurence B. Milstein,et al.  A concatenated decoding scheme for (1-D) partial response with matched spectral-null coding , 1993, Proceedings of GLOBECOM '93. IEEE Global Telecommunications Conference.

[175]  Masafumi Tamura,et al.  High‐density magnetic tape recording by a nontracking method , 1993 .

[176]  Steven W. McLaughlin,et al.  Upper bounds on the capacity of the digital magnetic recording channel , 1993 .

[177]  Xiaodong Che,et al.  General analysis of noise in recorded transitions in thin film recording media , 1993 .