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Some Codes That Combine ECC With Modulation

IP.com Disclosure Number: IPCOM000100598D
Original Publication Date: 1990-May-01
Included in the Prior Art Database: 2005-Mar-15
Document File: 2 page(s) / 60K

Publishing Venue

IBM

Related People

Blaum, M: AUTHOR

Abstract

Disclosed is an implementation of several codes that combine the processes of ECC with modulation. The traditional scheme used in magnetic recording consists of the concatenation of an error-correcting code followed by a modulation code. The new codes have better performance in noisy channels strongly dominated by random errors. The encoding and decoding procedures are simple and can be adapted to the traditional scheme.

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Some Codes That Combine ECC With Modulation

       Disclosed is an implementation of several codes that
combine the processes of ECC with modulation.  The traditional scheme
used in magnetic recording consists of the concatenation of an
error-correcting code followed by a modulation code.  The new codes
have better performance in noisy channels strongly dominated by
random errors.  The encoding and decoding procedures are simple and
can be adapted to the traditional scheme.

      We use a set of 2*n symbols, to be denoted r(m;d,k). The set
r(m;d,k) is a set of binary m-tuples such that, each m-tuple verifies
the (d,k) constraints and any concatenation of m-tuples also verifies
the (d,k) constraints. We want n to be as large as possible.  The
elements in r(m;d,k) will be identified with the elements in GF(2*n).
 In this way, we provide a natural encoder from binary n-tuples to
modulated symbols in r(m;d,k). More specifically, the identification
between symbols in r(m;d,k) and symbols in GF(2*n) is provided by a
1-1 function f, f:r(m;d,k)TGF(2*n).

      This identification allows to construct codes over GF(2*n). We
use the family of Reed Solomon codes (1).  Let C be a Reed Solomon
code over GF(2*n) of length N and redundancy R, i.e., the code can
correct up to (N-R)/2 bytes in error (1). The encoding is given by
the following algorithm:
      Encoding Algorithm:
      Let (a1,a2, ... ,aK), where aieGF(2*n) for
      1&i&K be an information string. Then:
      I. Encode (a1,a...