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Array combinatorial decoding with multiple error and erasure detection and location using cyclic equivalence testing

  • US 5,644,695 A
  • Filed: 07/15/1994
  • Issued: 07/01/1997
  • Est. Priority Date: 01/03/1994
  • Status: Expired due to Fees
First Claim
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1. In a computer system comprising a central processing unit and a storage medium, a method for detecting and locating up to two symbols in error or erasures in an n×

  • mA (n,m,4) parity coded bit array where n is a prime number, m≦

    n comprising the steps of;

    (a) rotating, using said computer system, m column vectors in said n×

    m A(n,m,4) parity coded bit array by predetermined amounts;

    (b) forming, using said computer system, m modulo 2 summed syndromes from said rotated m column vectors, and in a presence of any error, deriving at least one non-zero syndrome;

    (c) computing, using said computer system, first, second, and third test vectors, each test vector being a modulo 2 sum of a unique selected syndrome and a unique selected rotated syndrome; and

    (d) initializing, using said computer system, a tracking variable L and incrementing L for each repetition of step (d) and;

    (1) either providing signal indication of exactly one error at a column location defined by L in a presence of first and second null test vectors,(2) providing signal indication of exactly two errors and said two errors'"'"' column locations in a presence of the second test vector, said second test vector being equivalent of the first test vector rotated by L positions and the third test vector being equivalent of the second test vector rotated by K positions, L<

    K,(3) repeating steps (d) in an absence of cyclic equivalence among the test vectors, or(4) providing signal indication of more than two errors either in a presence of at least two zero test vectors or when L=m.

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