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Method for Analyzing the Noise in a Magnetic Recording Channel Corrupted by Additive Gaussian Noise And Jitter

IP.com Disclosure Number: IPCOM000099429D
Original Publication Date: 1990-Jan-01
Included in the Prior Art Database: 2005-Mar-14
Document File: 2 page(s) / 56K

Publishing Venue

IBM

Related People

Feig, E: AUTHOR

Abstract

For a given input sequence bk:k=1,2, ...., B of plus and minus ones, the analog output of a Class IV Partial Response channel corrupted by additive noise and jitter, when the jitter is moderate, is well approximated as:

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This is the abbreviated version, containing approximately 63% of the total text.

Method for Analyzing the Noise in a Magnetic Recording Channel Corrupted by Additive Gaussian Noise And Jitter

       For a given input sequence bk:k=1,2, ...., B of plus and
minus ones, the analog output of a Class IV Partial Response channel
corrupted by additive noise and jitter, when the jitter is moderate,
is well approximated as:

      where h(t) is the channel response to a dibit input, and
ak=1/2(bk-bk-1).  The sample's values observed at times t=nT are:

      where aW is the vector whose entries are the akWk ordered
sequentially. h'n is the vector with entries h'((k-n)T), and $
denotes the vector inner product.  The noise is well approximated as
follows:  w(t) is Gaussian (perhaps colored) with covariance matrix
CW, and Wk is a sequence of random variables normally distributed
about O with variance 2. W

      When the input data is a sequence of alternating plus and minus
ones, then the noise is stationary with covariance matrix: where CW =
HHt, with H the Toeplitz matrix whose i,j-th entry is h'((i-j)T), and
where the superscript t denotes the matrix transpose.

      When the input data is a random sequence of plus and minus
ones, then the noise is no longer stationary.  But the number of
consecutive same signs in the random sequence is approximately equal
to the number of consecutive opposite signs, and so the output has a
stable averaged noise statistic which is the same as that of a
channel with stationary statistics with covariance...