Viterbi Detection

  • Jan W. M. Bergmans


In Chapter 3 we have observed that maximum-likelihood detection of a data sequence in the presence of ISI and noise becomes enormously complicated for long messages when done in a ‘brute-force’ manner. In the present chapter we develop the Viterbi detector (VD), which performs maximum-likelihood detection in a much more efficient fashion. Basic to the VD is a technique called dynamic programming that we introduce in Section 7.2 with the aid of an example. Dynamic programming originated as a solution to the classical shortest path problem, but can also be tailored to data detection (Sections 7.3 and 7.4). The recursive nature of the technique causes total processing effort to grow only linearly with the message length, as opposed to the exponential growth for the ‘brute-force’ receiver of Chapter 3.


Viterbi Algorithm Detection Delay Decision Feedback Equalizer Viterbi Decoder Memory Length 
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  1. [1]
    K. Abend and B.D. Fritchmann, `Statistical Detection for Communication Channels with Intersymbol Interference’, Proc. IEEE, Vol. 58, pp. 779–785, May 1970.CrossRefGoogle Scholar
  2. [2]
    J.B. Anderson and S. Mohan, `Sequential Decoding Algorithms: A Survey and Cost Analysis’, IEEE Trans. Commun., Vol. COM-32, pp. 169–176, Feb. 1984.Google Scholar
  3. [3]
    C.T. Beare, `The Choice of the Desired Impulse Response in Combined Linear-Viterbi Algorithm Equalizers’, IEEE Trans. Commun., Vol. COM-26, pp. 1301–1307, Aug. 1978.Google Scholar
  4. [4]
    J.W.M. Bergmans and Y.C. Wong, ‘A Simulation Study of Intersymbol Interference Cancellation’, AEÜ (Electronics and Communication), Vol. 41, No. 1, pp. 33–37, 1987.Google Scholar
  5. [5]
    J.W.M. Bergmans, S.A. Rajput and F.A.M. van de Laar, `On the Use of Decision Feedback for Simplifying the Viterbi Detector’, Philips J. Res., Vol. 42, No. 4, pp. 399–428, 1987.Google Scholar
  6. [6]
    J.W.M. Bergmans, S. Mita and M. Izumita, `Receiver for Data Transmission System with Nonlinearities’, U.S. patent no. 5,131,011, Jul. 14, 1992.Google Scholar
  7. [7]
    J.W.M. Bergmans, K.D. Fisher and H.W. Wong-Lam, `Variations on the Ferguson Viterbi Detector’, Philips J. Res., Vol. 47, No. 6, pp. 361–386, 1993.Google Scholar
  8. [8]
    J.W.M. Bergmans, F.M.J. Willems and G.S.M. Kerpen, `On the Performance of Data Receivers with a Restricted Detection Delay’, IEEE Trans. Commun., Vol. 42, No. 6, pp. 2315–2324, June 1994.CrossRefGoogle Scholar
  9. J.W.M. Bergmans and J.O. Voorman, `Dual Decision Feedback Equalizer’, submitted to IEEE Trans. Commun.,1996.Google Scholar
  10. [10]
    H. Burkhardt and L.C. Barbosa, `Contributions to the Application of the Viterbi Algorithm’, IEEE Trans. Inform. Theory, Vol. IT-31, No. 5, pp. 626–634, Sept. 1985.MathSciNetGoogle Scholar
  11. [11]
    P.R. Chevillat and E. Eleftheriou, `Decoding of Trellis-Encoded Signals in the Presence of Intersymbol Interference and Noise’, IEEE Trans. Commun., Vol. COM-37, No. 7, pp. 669–676, Jul. 1989.Google Scholar
  12. [12]
    A.P. Clark and S.N. Abdullah, `Near-Maximum-Likelihood Detectors for Voiceband Channels’, IEE Proc., Pt. F, Vol. 132, No. 6, pp. 485–490, Oct. 1985.Google Scholar
  13. [13]
    E. Dahlman and B. Gudmundson, `Performance Improvement in Decision Feedback Equalisers by Using `Soft Decision“, Electronics Lett., Vol. 24, No. 17, pp. 1084–1085, Aug. 1988.CrossRefGoogle Scholar
  14. [14]
    A. Duel-Hallen and C. Heegard, `Delayed Decision-Feedback Sequence Estimation’, IEEE Trans. Commun., Vol. COM-37, No. 5, pp. 48–436, May 1989.Google Scholar
  15. [15]
    J. Erfanian, S. Pasupathy and G. Gulak, `Reduced Complexity Symbol Detectors with Parallel Structures for ISI Channels’, IEEE Trans. Commun., Vol. COM-42, No. 2/3/4, pp. 1661–1671, Feb./March/Apr. 1994.Google Scholar
  16. [16]
    V.M. Eyuboglu and S.U.H. Qureshi, `Reduced-State Sequence Estimation with Set Partitioning and Decision Feedback’, IEEE Trans. Commun., Vol. COM-36, No. 1, pp. 13–20, Jan. 1988.Google Scholar
  17. [17]
    D.D. Falconer and F.R. Magee, Jr., `Adaptive Channel Memory Truncation for Maximum Likelihood Sequence Estimation’, Bell Syst. Tech. J., Vol. 52, No. 9, pp. 1541–1562, Nov. 1973.zbMATHGoogle Scholar
  18. [18]
    M.J. Ferguson, `Optimal Reception for Binary Partial Response Channels’, Bell Syst. Tech. J., Vol. 51, No. 2, pp. 493–505, Feb. 1972.zbMATHGoogle Scholar
  19. [19]
    G. Fettweis and H. Meyr, `Parallel Viterbi algorithm Implementation: Breaking the ACS Bottleneck’, IEEE Trans. Commun., Vol. COM-37, No. 8, pp. 785–790, Aug. 1989.Google Scholar
  20. [20]
    G. Fettweis, `Algebraic Survivor Memory Management Design for Viterbi Decoders’, IEEE Trans. Commun., Vol. 43, No. 9, pp. 2458–2463, Sept. 1995.CrossRefGoogle Scholar
  21. [21]
    G. Feygin and P.G. Gulak, `Architectural Tradeoffs for Survivor Sequence Memory Management in Viterbi Decoders’, IEEE Trans. Commun., Vol. COM-41, No. 3, pp. 425–429, March 1993.Google Scholar
  22. [22]
    G.D. Forney, Jr., `Lower Bounds on Error Probability in the Presence of Large Intersymbol Interference’, IEEE Trans. Commun., Vol. COM-20, No. 2, pp. 76–78, Feb. 1972.Google Scholar
  23. [23]
    G.D. Forney, Jr., `Maximum-Likelihood Sequence Estimation of Digital Sequences in the Presence of Intersymbol Interference’, IEEE Trans. Inform. Theory, Vol. IT-18, No. 3, pp. 363–378, May 1972.MathSciNetGoogle Scholar
  24. [24]
    G.D. Forney, Jr., `The Viterbi Algorithm’, Proc. IEEE, Vol. 61, No. 3, pp. 268–278, March 1973.MathSciNetCrossRefGoogle Scholar
  25. [25]
    S.A. Fredricsson, `Joint Optimization of Transmitter and Receiver Filters in Digital PAM Systems with a Viterbi Detector’, IEEE Trans. Inform. Theory, Vol. IT-22, No. 2, pp. 200210, Mar. 1976.Google Scholar
  26. [26]
    A. Gersho and T.L. Lim, `Adaptive Cancellation of Intersymbol Interference for Data Transmission’, Bell Syst. Tech. J., Vol. 60, No. 11, pp. 1997–2021, Nov. 1981.Google Scholar
  27. [27]
    R.D. Gitlin and E.Y. Ho, `A Null-Zone Decision Feedback Equalizer Incorporating Maximum-Likelihood Bit Detection’, IEEE Trans. Commun., Vol. COM-23, No. 11, pp. 1243–1250, Nov. 1975.Google Scholar
  28. [28]
    N.H. Gottfried, `Low Complexity Viterbi Detector for Magnetic Disc Drives’, IEE Proc.E, Vol. 140, No. 1, pp. 78–80, Jan. 1993.Google Scholar
  29. [29]
    P.G. Gulak and T. Kailath, `Locally Connected VLSI Architectures for the Viterbi Algorithm’, IEEE J. Selected Areas Commun., Vol. SAC-6, No. 3, pp. 527–537, Apr. 1988.Google Scholar
  30. [30]
    A.P. Hekstra, `An Alternative to Metric Rescaling in Viterbi Decoders’, IEEE Trans. Cammun., Vol. COM-37, No. 11, pp. 1220–1222, Nov. 1989.Google Scholar
  31. [31]
    A.P. Hekstra, `On the Numerical Range of the Path Metrics in a Binary Viterbi Decoder’, to appear in IEEE Trans. Inform. Theory.Google Scholar
  32. [32]
    R. Karabed and P. Siegel, `Matched Spectral-Null Codes for Partial-Response Channels’, IEEE Trans. Inform. Theory, Vol. IT-37, No. 3, pt. II, pp. 818–855, May 1991.Google Scholar
  33. [33]
    G. Kawas-Kaleh, `Double Decision Feedback Equalizer’, Frequenz, Vol. 33, No. 5, pp. 146–149, 1979.CrossRefGoogle Scholar
  34. [34]
    H. Kobayashi, `Application of Probabilistic Decoding to Digital Magnetic Recording Systems’, IBM J. Res. Develop., pp. 64–74, Jan. 1971.Google Scholar
  35. R. Kohno, H. Imai, and M. Hatori, `Automatic Equalizer Including a Decoder of Error-Correcting Code and Its Development’, Electron. and Commun. in Japan,Pt. I, Vol. 68, No. 11, pp. 66–77, 1985.Google Scholar
  36. [36]
    H. Kubo, K. Murakami and T. Fujino, `An Adaptive Maximum-Likelihood Sequence Estimator for Fast Time-Varying Intersymbol Interference Channels’, IEEE Trans. Commun., Vol. COM-42, No. 2/3/4, pp.. 1872–1880, Feb./March/Apr. 1994.Google Scholar
  37. [37]
    H.-D Lin and D.G. Messerschmitt, `Parallel Viterbi Decoding Methods for Uncontrollable and Controllable Sources’, IEEE Trans. Commun., Vol. COM-41, No. 1, pp. 62–69, Jan. 1993.Google Scholar
  38. [38]
    L.R. MacKechnie, `Maximum-Likelihood Receivers for Channels Having Memory’, Ph.D. Dissertation, Dep. Elec. Eng., Univ. of Notre Dame, Notre Dame, Jan. 1973.Google Scholar
  39. [39]
    F.R. Magee, Jr. and J.G. Proakis, `An Estimate of the Upper Bound on Error Probability for Maximum-Likelihood Sequence Estimation on Channels Having a Finite-Duration Pulse Response’, IEEE Trans. Inform. Theory, Vol. TT-19, pp. 699–702, Sept. 1973.Google Scholar
  40. K. Matsushita, A. Iketani, A. Ide and C. Yamamitsu, `Path Feedback Viterbi Detection Without Open Eye Patterns’, IEEE Transi. J. on Magn. in Japan,Vol. 3, No. 8, pp. 642652, Aug. 1988.Google Scholar
  41. [41]
    D.G. Messerschmitt, `A Geometric Theory of Intersymbol Interference - Part II: Performance of the Maximum-Likelihood Detector’, Bell Syst. Tech. J., Vol. 52, No. 9, pp. 15211539, Nov. 1973.Google Scholar
  42. [42]
    S. Mita, M. Izumita, N. Doi and Y. Eto, `Automatic Equalizer for Digital Magnetic Recording Systems’, IEEE Trans. Magn., Vol. MAG-23, No. 5, pp. 3672–3674, Sept. 1987.CrossRefGoogle Scholar
  43. [43]
    C.S. Modlin and J.M. Cioffi, `Reduced-State Nonlinear Equalization for Magnetic Storage’, Proc. GLOBECOM’94, pp. 1134–1138, San Fransisco, Nov. 28 - Dec. 2, 1994.Google Scholar
  44. [44]
    J. Moon and L.R. Carley, `Performance Comparison of Detection Methods in Magnetic Recording’, IEEE Trans. Magn., Vol. MAG-26, No. 6, pp. 3155–3172, Nov. 1990.Google Scholar
  45. [45]
    R.E. Morley, Jr. and D.L Snyder, `Maximum Likelihood Sequence Estimation for Randomly Dispersive Channels’, IEEE Trans. Commun., Vol. COM-27, No. 6, pp. 833–839, June 1979.Google Scholar
  46. [46]
    S. Mueller and J. Salz, `A Unified Theory of Data-Aided Equalization’, Bell Syst. Tech. J., Vol. 60, No. 9, pp. 2023–2038, Nov. 1981.Google Scholar
  47. [47]
    S. Ölçer, `Reduced-State Sequence Detection of Multilevel Partial-Response Signals’, IEEE Trans. Commun., Vol. COM-40, No. 1, pp. 3–6, Jan. 1992.Google Scholar
  48. [48]
    J.K. Omura, `On Optimum Receivers for Channels with Intersymbol Interference’, (Abstract), presented at the IEEE Int. Symp. Information Theory, Noordwijk, Holland, June 1970.Google Scholar
  49. [49]
    A.M. Patel, `A New Digital Signal Processing Channel for Data Storage Products’, IEEE Trans. Magn., Vol. MAG-27, No. 6, pp. 4579–4584, Nov. 1991.Google Scholar
  50. [50]
    A.M. Patel, R.A. Rutledge, and B.S. So, `Performance Data for a Six-Sample Look-Ahead (1,7)ML Detection Channel’, IEEE Trans. Magn., Vol. MAG-29, pp. 4012–4014, Nov. 1993.Google Scholar
  51. [51]
    S.U. Qureshi and E.E. Newhall, `An Adaptive Receiver for Data Transmission over Time-Dispersive Channels’, IEEE Trans. Inform. Theory, Vol. IT-19, pp. 448–457, July 1973.Google Scholar
  52. [52]
    C.M. Rader, `Memory Management in a Viterbi Decoder’, IEEE Trans. Commun., Vol. COM-29, No. 9, pp. 1399–1401, 1981.Google Scholar
  53. [53]
    A. Sano and J.-I. Yamazaki, `Generalized Decision Feedback Equalizer for Approximate Maximum-Likelihood Bit Detection of Digital Signals’, Int J. Electronics, Vol. 52, No. 2, pp. 167–176, 1982.CrossRefGoogle Scholar
  54. [54]
    R.C. Schneider, `Sequence (Viterbi-Equivalent) Decoding’, IEEE Trans. Magn., Vol. MAG-26, No. 6, pp. 2539–2541, Nov. 1988.Google Scholar
  55. [55]
    C. B. Shung, P.H. Siegel, G. Ungerboeck and H.K. Thapar, `VLSI Architectures for Metric Normalization in the Viterbi Algorithm’, Proc. ICC’90, Apr. 16–19, 1990, pp. 1723–1728.Google Scholar
  56. [56]
    C.B. Shung, H.-D. Lin, R. Cypher, P.H. Siegel, and H.K. Thapar, `Area-Efficient Architectures for the Viterbi Algorithm–Part I: Theory’, IEEE Trans. Commun., Vol. COM-41, No. 4, pp. 636–644, Apr. 1993.Google Scholar
  57. [57]
    C.B. Shung, H.-D. Lin, R. Cypher, P.H. Siegel, and H.K. Thapar, `Area-Efficient Architectures for the Viterbi Algorithm–Part H: Applications’, IEEE Trans. Commun., Vol. COM41, No. 5, pp. 802–807, May 1993.Google Scholar
  58. [58]
    P.H. Siegel, C.B. Shung, T.D. Howell, and H.K. Thapar, `Exact Bounds for Viterbi Detector Path Metric Differences’, Proc. ICASSP’91, pp. 1093–1096, May 13–16, 1991.Google Scholar
  59. [59]
    R.R. Spencer and P.J. Hurst, `Analog Implementations of Sampling Detectors’, IEEE Trans. Magn., Vol. MAG-27, No. 6, pp. 4516–4521, Nov. 1991.CrossRefGoogle Scholar
  60. [60]
    H.K. Thapar and J.M. Cioffi, `A Block Processing Method for Designing High-Speed Viterbi Detectors’, Proc. ICC’89, Boston, USA, June 11–14, 1989, pp. 1096–1100.Google Scholar
  61. [61]
    W. Turin, `Union Bounds on Viterbi Algorithm Performance’, ATandT Techn. J., Vol. 64, No. 10, pp. 2375–2385, Dec. 1985.MathSciNetGoogle Scholar
  62. [62]
    G. Ungerboeck, `Adaptive Maximum-Likelihood Receiver for Carrier-Modulated Data-Transmission Systems’, IEEE Trans. Commun., Vol. COM-22, No. 5, pp. 624–636, May 1974.Google Scholar
  63. [63]
    G. Ungerboeck, `Channel Coding with Multilevel/Phase signals’, IEEE Trans. Inform. Theory, Vol. IT-28, No. 1, pp. 55–67, Jan. 1982.Google Scholar
  64. [64]
    F.L. Vermeulen and M.E. Hellman, `Reduced State Viterbi Decoders for Channels with Intersymbol Interference’, Proc. ICC’74, Minneapolis, MN, pp.37B-1 to 37B - 9, June 1974.Google Scholar
  65. [65]
    A.J. Viterbi, `Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm’, IEEE Trans. Inform. Theory, Vol. IT-13, pp. 260–269, Apr. 1967.Google Scholar
  66. [66]
    A.J. Viterbi and J.K. Omura, Principles of Digital Communication and Coding. Tokyo: McGraw-Hill Kogakusha, Ltd., 1979.Google Scholar
  67. [67]
    D. Welland et al., `Implementation of a Digital Read/Write Channel with EEPR4 Detection’, IEEE Trans. Magn., Vol. MAG-31, No. 2, pp. 1180–1185, March 1995.Google Scholar
  68. [68]
    K.A. Wen and J.Y. Lee, `Parallel Processing for Viterbi Algorithm’, Electronics Lett., Vol. 24, No. 17, pp. 1098–1099, Aug. 1988.CrossRefGoogle Scholar
  69. [69]
    K. Wesolowski and J.G. Proakis, `A Simplified Two-Stage Equalizer with a Reduced Number of Multiplications for Data Transmission over Voiceband Telephone Links’, IEEE J. Selected Areas Commun., Vol. SAC-2, No. 5, pp. 731–742, Sept. 1984.Google Scholar
  70. [70]
    K. Wesolowski, `On the Performance and Convergence of the Adaptive Canceller of Inter-symbol Interference in Data Transmission’, IEEE Trans. Commun., Vol. COM-33, No. 5, pp. 425–432, May 1985.Google Scholar
  71. [71]
    K. Wesolowski, `An Efficient DFEandML Suboptimum Receiver for Data Transmission over Dispersive Channels Using Two-Dimensional Signal Constellations’, IEEE Trans. Commun., Vol. COM-35, No. 3, pp. 336–339, Mar. 1987.Google Scholar
  72. [72]
    R.W. Wood, `Viterbi Detection of Miller-Squared Code on a Tape Channel’, Int. Conf. on Video, Audio and Data Recording, IERE Conf. Proc. 54, Southampton, England, Apr. 20–23, 1982, pp. 333–344.Google Scholar
  73. [73]
    R.W. Wood and D.A. Petersen, `Viterbi Detection of Class IV Partial Response on a Magnetic Recording Channel’, IEEE Trans. Commun., Vol. COM-34, no. 5, pp. 454–461, May 1986.Google Scholar
  74. [74]
    R.W. Wood, `New Detector for 1,k Codes Equalized to Class II Partial Response’, IEEE Trans. Magn., Vol. MAG-25, pp. 4075–4077, Sept. 1989.Google Scholar
  75. [75]
    R.W. Wood, `Magnetic Megabits’, IEEE Spectrum, pp. 32–38, May 1990.Google Scholar
  76. [76]
    R.W. Wood, `Enhanced Decision Feedback Equalization’, IEEE Trans. Magn., Vol. MAG-26, No. 5, pp. 2178–2180, Sept. 1990.Google Scholar
  77. [77]
    J.M. Wozencraft and I.M. Jacobs, Principles of Communication Engineering. New York: Wiley, 1965.Google Scholar
  78. [78]
    A. Yamashita, T. Nakamura, Y. Tozawa, T. Katoh and M. Moriwake, `A New Path Memory for Viterbi Decoders’, Proc. GLOBECOM’87, pp. 2076–2079.Google Scholar

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© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Jan W. M. Bergmans
    • 1
  1. 1.Philips ResearchEindhovenThe Netherlands

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