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Decoder Algorithm for Class IV Partial Response Magnetic Recording System With Nonlinear Distortion

IP.com Disclosure Number: IPCOM000034841D
Original Publication Date: 1989-Apr-01
Included in the Prior Art Database: 2005-Jan-27
Document File: 3 page(s) / 48K

Publishing Venue

IBM

Related People

Feig, E: AUTHOR

Abstract

A decoding algorithm for class IV partial response magnetic recording systems with nonlinear distortion is provided. The decoding algorithm first samples the output of the channel at twice the rate of a Partial Response Maximum Likelihood decoder and utilizes a standard Viterbi algorithm to estimate the data sequence. The data sequence estimate is used to estimate the jitter. The jitter estimate is then subtracted from the sampled values, and another standard Viterbi algorithm is utilized on the difference to obtain a final estimate of the data sequence.

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Decoder Algorithm for Class IV Partial Response Magnetic Recording System With Nonlinear Distortion

A decoding algorithm for class IV partial response magnetic recording systems with nonlinear distortion is provided. The decoding algorithm first samples the output of the channel at twice the rate of a Partial Response Maximum Likelihood decoder and utilizes a standard Viterbi algorithm to estimate the data sequence. The data sequence estimate is used to estimate the jitter. The jitter estimate is then subtracted from the sampled values, and another standard Viterbi algorithm is utilized on the difference to obtain a final estimate of the data sequence. The provided decoding algorithm, while not guaranteeing Maximum Likelihood decoding, and while requiring use of the standard Viterbi algorithm twice plus some additional computation, has an error rate several orders of magnitude better than that of "blind" Viterbi decoding and is desirable in high signal-to-noise environments. The output of an ideal Class IV Partial Response channel with NRZI recording without nonlinear distortion takes the form: y-(t) = k ak h(t - kT) + w(t) (1) where T is the sampling rate, w(t) is Gaussian noise with zero mean, ak are coefficients taking values +1 or -1, and h(t) is: sin(f/T) sin[f(t - 2T)/T]

h(t) = (2)

ft/T f(t - 2T)/T When bits are linearly packed very densely, the position of a transition is affected by the presence of a transition one bit interval earlier. The nonlinear distortion in the system is well approximated by: y(t) = k ak h(t - kT - ewk) + w(t) (3) where

wk = (ak - ak-1)(ak-1 - ak-2)/4 (4) For small values of e, the function h(t) is well approximated by the first two terms of the Taylor series, and hence y(t) = k ak h{(t - kT + e) - (e + ewk)} + w(t) (5) = k ak {h(t - kT + e) + (e + ewk)h'(t - kT + e)} + w(t) (6) If v(t) = y (t - e) (7) then v(t) = k akh(t-kT) + e k akh'(t-kT) + e k akwkh'(t-kT) + w(t-e) (8) Also, if L(t) = k ak h(t - kT) (9) and

N(t) = k akwkh'...