Forward Chien search type Reed-Solomon decoder circuit

A Reed-Solomon decoder, comprising:

• a syndrome generator circuit to generate a syndrome polynomial from input data;
• an erasure generator circuit to receive the syndrome polynomial and a TA flag and to generate an erasure polynomial;
• an modified Euclid algorithm (MEA) circuit to receive the syndrome polynomial and the erasure polynomial, and to output an error location polynomial function and an error pattern polynomial function;
• a Chien search circuit to receive the error location polynomial function, to perform a Chien search, and find an error location;
• a Forney algorithm circuit to receive the error pattern polynomial function and find an error pattern by application of a Forney algorithm;
• and
• a seed generator circuit to generate a Galois Field (GF) value when the Chien search is performed, and indicate a seed value corresponding to a codeword length.

An error check and correction circuit, comprising:

• a Reed-Solomon decoder including a Chien search circuit, a Forney algorithm circuit and a seed generator circuit;
• and
• a cyclic redundancy check (CRC) operator circuit to determine miss-correction of an error by the Reed-Solomon decoder,
• wherein the Chien search circuit receives an error location polynomial function, performs Chien search, and finds an error location;
• the Forney algorithm circuit receives an error pattern polynomial function, and finds an error pattern by application of a Forney algorithm;
• and
• the seed generator circuit providing a seed value corresponding to a codeword length for input data when the Chien search is performed, and obtaining and outputting exponential terms for polynomials associated with at least one of the error location polynomial function and the error pattern polynomial function,
• wherein the Chien search is performed in the same computational direction as an order for the input data;
• and
• whenever an error pattern value for an error location is generated in the Chien search, the error pattern value is input to the Chien search so that a CRC operation is simultaneously performed.

A method of checking and correcting an error in input data, the method comprising:

• generating an error location polynomial from the input data;
• generating an error pattern polynomial from the input data;
• sequentially multiplying a seed value corresponding to a codeword related to the input data, and calculating variable terms of the polynomials;
• performing a Chien search based on the error location polynomial and the seed value to obtain an error location;
• applying a Forney algorithm in relation to the error pattern polynomial and the seed value to obtain an error pattern;
• and
• correcting the error in the input data in relation to the error location and the error pattern.

A method of implementing Reed-Solomon (RS) coding, comprising:

• performing cyclic redundancy check (CRC) following RS decoding;
• wherein the RS decoding comprises sequentially multiplying a seed value corresponding to a codeword related to the input data, and calculating variable terms of an error location polynomial;
• and
• performing a Chien search based on the based on the error location polynomial and the seed value.