Combined error position circuit and chien search circuit for reed-solomon decoding

A programmable logic device, comprising:

• control circuitry, for receiving program instructions and for generating control signals responsive thereto;
• a data bus;
• and
• a combined Chien search and error position execution unit coupled to the data bus, for executing a Chien search and error position instruction under the control of the control circuitry, and comprising:
• a root detection circuit, for sequentially evaluating an error locator polynomial corresponding to a plurality of data words corresponding to error locator polynomial coefficients, for each of a plurality of elements in a finite field, and for generating a zero signal responsive to identifying a root of the error locator polynomial;
• an error position register comprising a plurality of stages, each of the error position register stages having a data input and having a control input;
• a decoder, coupled to the root detection circuit and to the error position register, for sequentially enabling the plurality of error position register stages responsive to the root detection circuit generating the zero signal;
• an index counter for generating a count corresponding to the member of a finite field for which the root detection circuit is evaluating the error locator polynomial;
• and
• a subtractor for subtracting the count from a constant corresponding to the number of members of the finite field, the subtractor having an output coupled to the data input of each of the plurality of register stages of the error position register stages.

A method of operating a logic circuit to generate error position indicator terms in Reed-Solomon decoding, comprising the steps of:

• evaluating an error locator polynomial for each of a plurality of members of a finite field;
• during the evaluating step, maintaining a count value corresponding to the one of the plurality of members for which the evaluating step is being performed;
• subtracting the count value from a maximum value corresponding to the number of members of the finite field to produce a position value;
• and
• responsive to the evaluating step identifying a root of the error locator polynomial, storing the position value into a selected one of a plurality of error position register stages.