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Method of code generation that minimizes error propagation

  • US 7,676,725 B1
  • Filed: 02/27/2006
  • Issued: 03/09/2010
  • Est. Priority Date: 02/27/2006
  • Status: Active Grant
First Claim
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1. A method of generating a code that minimizes error propagation, comprising the steps of:

  • a) selecting an integer m, where m represents a length of unencoded bits;

    b) selecting an integer n, where n represents a length of encoded bits, and where n>

    m;

    c) selecting a range of fractions od, where od represents a range of density values of one bits;

    d) selecting in a transmission system an integer mrl, where mrl represents a maximum run length of bits;

    e) generating an encoding map M, where each representation of 2^m bits is mapped to a unique representation in 2^n, and wherein the unique representations in 2^n to which the representations in 2^m are mapped satisfy od and mrl;

    f) generating a decoding map N, where each representation of 2^n bits is mapped to a representation in 2^m as follows;

    a. mapping each representation of 2^n bits that appears in the encoding map M to the representation of 2^m bits to which it is mapped in the encoding map M; and

    b. mapping each representation of 2^n bits that does not appear in the encoding map according to the following steps;

    i. determining the minimum hamming distance between the representation of 2^n bits and the representations of 2^n bits that appear in the encoding map M;

    ii. determining the representations of 2^n bits that appear in the encoding map M that are within the Hamming distance determined in step (i) to the representation of 2^n bits that does not appear in the encoding map M;

    iii. determining the representations in 2^m bits that correspond to the representation in 2^n bits determined in step (ii);

    iv. determining a bit-majority, if any, in each bit position of the representations of 2^m bits determined in step (iii);

    v. if a bit-majority is not found for a bit position then setting the bit position to the bit-majority, if any, of all of the bits in the representations on 2^m bits determined in step (iii);

    vi. if a bit-majority is not found then setting the bit position to zero; and

    vii. mapping the representation of 2^n bits that does not appear in the encoding map M to the bit-majority bits determined in steps (iv), (v), and (vi);

    g) determining an error-propagation score for encoding map M and decoding map N; and

    h) returning to step (e) if a user requires an encoding map M and a decoding map N with a lower error-propagation score than the error-propagation score determined in step (g).

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