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Method and apparatus for determining the coefficients of a locator polynomial

Image Number 3 for United States Patent #4845713.

For decoding a Reed-Solomon codeword with (n-K) check characters an error/erasure locator (32) executes a codeword cycle comprising (n-K) "coefficient" iterations followed by (n-K) "modified syndrome" iterations. The error/erasure locator (32) includes a bank (52) of simultaneously loadable syndrome registers and a bank (56) of coefficient registers. The syndrome registers are connected to one another in a circular shift path (91). The error/erasure locator (32) further includes a cascading arrangement of PISO multipliers (54), a SIPO multiplier (60), and PISO multipliers (61). The PISO multipliers (54) operate upon the contents of the syndrome registers (52) (expressed in a conventional basis representation) and the contents of the coefficient register (56) (expressed in dual basis representation) to obtain a serial current discrepancy d.sub.n. The SIPO multiplier 60 multiplies the serial current discrepancy d.sub.n by a parallel-formatted multiplicative inverse d.sub.m.sup.-1 .beta..sub.i of a prior discrepancy (expressed in dual basis representation) to obtain in one set of clock cycles, the product d.sub.n d.sub.m.sup.-1. During a second set of clock cycles the discrepancy product d.sub.n d.sub.m.sup.-1 is further multiplied using a second bank (61) of PISO multipliers by the contents of corresponding auxiliary registers (62) to obtain a serial product useful for updating the coefficient registers (56). The syndrome registers (52) perform the dual purpose of storing the original syndromes during the coefficient iteration and of storing the modified syndromes produced during the modified syndrome iteration.

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