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Constrained Channel Coding With Spectral Null

IP.com Disclosure Number: IPCOM000047261D
Original Publication Date: 1983-Oct-01
Included in the Prior Art Database: 2005-Feb-07
Document File: 5 page(s) / 29K

Publishing Venue

IBM

Related People

Langdon, GG: AUTHOR [+3]

Abstract

This invention relates to a method for the definition of a Finite State Machine (FSM) for a constrained channel giving a spectral null at f/n and which has a manageable number of internal states. A second object is to show how a combination of coding techniques from the prior art may be employed, together with an approximation step, to encode and decode channel strings. In the prior art, discrete constrained channels such as for magnetic recording are studied. A channel clock measures channel time units of a given duration, the reciprocal of that duration being clock frequency "f". A spectral null at "f/n" occurs at a frequency whose period is "n" clock times. The signal amplitude is a(i) at clock time i.

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Constrained Channel Coding With Spectral Null

This invention relates to a method for the definition of a Finite State Machine (FSM) for a constrained channel giving a spectral null at f/n and which has a manageable number of internal states. A second object is to show how a combination of coding techniques from the prior art may be employed, together with an approximation step, to encode and decode channel strings. In the prior art, discrete constrained channels such as for magnetic recording are studied. A channel clock measures channel time units of a given duration, the reciprocal of that duration being clock frequency "f". A spectral null at "f/n" occurs at a frequency whose period is "n" clock times. The signal amplitude is a(i) at clock time i. In the past, Fourier techniques were employed to determine the component of a particular frequency f/n in a string of amplitudes A(i). The component has an amplitude and phase and was calculated as a point p in the complex plane. The coordinates of p were x(p),jy(p), where "j" was the imaginary number, square root of minus
1. The amplitude at frequency f/n was the distance from the origin of the complex plane and the point p. The complex plane point p corresponding to a frequency f/n over a particular sequence of amplitudes a = A(1),A(2),...,A(m) is: p(a) = S/m/A(i) x sin(2Fif/n) + j cos(2Fi/n) i=1 (1) In saturated magnetic recording, the amplitude values A(i) are either +1 or -1. The point on the complex plane may be determined recursively. If channel string u of duration |u| has led to point p(u) on the complex x plane, and symbol a of duration m and amplitudes A(1),A(2),...,A(m) follows, then p(u.a) = p(u) + S/m/ A(i) x sin(2F u +i/n) + j cos(2Fu +i/n) i=1 (2) where u.a denotes the concatenation of symbol a to string u. For the purposes of Eq. 1, since sine and cosine are periodic, only the time unit "|u| mod n" need be retained from one recursion to the next: u.a mod n = (u mod n + a ) mod n. The actual "state" s of the system has two components: point n the in the complex plane, and time |u| mod n. Like a "follower" machine to determine a point in the complex plane, however, it is used in this case in a different manner. Let there exist a 16x16 square of unit squares, each unit square having resolution 16x16 to give 65536 states. Let this rectangle in the complex plane be called the fine grid G. Grid G may be partitioned to form a coarse grid G' of fewer points. Function P A Function P takes the points on fine grid G and maps them to points to points on coarse grid G'. For purposes of this invention, round the last four (fractional) bits of each coordinate of points in G to give a set of 16x16 points of a coarse grid G'. Coarse grid G' of 1024 states is used as the states of a channel FSM. Next, there is defined the state transition function T'(s,a) which represents the constraints. Function T' on grid G' is called the driver FSM. From this point on, the code design procedure fol...