Editing Partial-response maximum-likelihood (section)

== Theoretical development ==
[[File:Class 4 Partial-Response Eye Diagram.jpg|thumb|Continuous-time Partial-Response (class 4) and corresponding 'eye pattern']]
'''Partial-response''' was first proposed by Adam Lender in 1963.<ref>A. Lender, "[https://ieeexplore.ieee.org/abstract/document/6373379 The duobinary technique for high-speed data transmission]", Trans. AIEE, Part I: Communication and Electronics, Vol. 82, No. 2, pp. 214-218, May 1963</ref> The method was generalized by Kretzmer in 1966. Kretzmer also classified the several different possible responses,<ref>E. Kretzmer, "[https://ieeexplore.ieee.org/document/1089288 Generalization of a Technique for Binary Data Communication]", IEEE Trans. Comm., Vol. 14, No. 1, pp. 67-68 Feb. 1966</ref> for example, PR1 is duobinary and PR4 is the response used in the classical PRML. In 1970, Kobayashi and Tang recognized the value of PR4 for the [[magnetic recording]] channel.<ref>H. Kobayashi and D. Tang, "[https://ieeexplore.ieee.org/document/5391640 Application of Partial-response Channel Coding to Magnetic Recording Systems]", IBM J. Res. Dev., Vol, 14, No. 4, pp. 368-375, July 1970</ref>

'''[[Maximum-likelihood]]''' decoding using the eponymous [[Viterbi algorithm]] was proposed in 1967 by [[Andrew Viterbi]] as a means of decoding [[convolutional codes]].<ref>A. Viterbi, "[https://ieeexplore.ieee.org/document/1054010 Error bounds for convolutional codes and an asymptotically optimum decoding algorithm]", IEEE Trans. Info. Theory, Vol. 13, No. 2, pp. 260-269, Apr. 1967</ref>

By 1971, [[Hisashi Kobayashi]] at [[IBM]] had recognized that the Viterbi algorithm could be applied to analog channels with inter-symbol interference and particularly to the use of PR4 in the context of Magnetic Recording<ref>H. Kobayashi, "[https://ieeexplore.ieee.org/document/1054689 Correlative level coding and maximum-likelihood decoding]", IEEE Trans. Inform. Theory, vol. IT-17, PP. 586-594, Sept. 1971</ref> (later called PRML). (The wide range of applications of the Viterbi algorithm is well described in a review paper by [[Dave Forney]].<ref>D. Forney, “[https://www2.isye.gatech.edu/~yxie77/ece587/viterbi_algorithm.pdf The Viterbi Algorithm]”, Proc. IEEE, Vol. 61, No. 3, pp. 268-278, Mar. 1973</ref>) A simplified algorithm, based upon a difference metric, was used in the early implementations. This is due to Ferguson at [[Bell Labs]].<ref>M. Ferguson, ”[https://ieeexplore.ieee.org/document/6774130 Optimal reception for binary partial response channels]” Bell Syst. Tech. J., vol. 51, pp. 493-505, Feb. 1972</ref>