Parallel decoding of a BCH encoded signal

A method for decoding a Bose-Chadhuri-Hocquenghem (BCH) encoded signal, the method comprises:

• receiving the BCH encoded signal in a binary polynomial format to produce a received polynomial;
• converting the received polynomial into a plurality of binary error identifying polynomials;
• for each of the plurality of binary error identifying polynomials having an odd index, dividing the received polynomial by a corresponding one of a plurality of minimum polynomials to obtain a quotient polynomial and a remainder polynomial during a given time interval, wherein the remainder polynomial represents one of the plurality of binary error identifying polynomials;
• recursively processing the plurality of remainder polynomials to produce a plurality of odd indexed syndrome components of a plurality of syndrome values;
• squaring each of the plurality of odd indexed syndrome components to produce a plurality of even indexed syndrome components of the plurality of syndrome values;
• processing the plurality of syndrome values to produce an error locator polynomial that represents errors in the received polynomial;
• evaluating the error locator polynomial to identify the bit location of the error in the BCH encoded signal;
• and
• correcting the BCH encoded signal based on the bit location of the error.

An apparatus for decoding a BCH encoded signal, the apparatus comprises:

• means for receiving the BCH encoded signal in a binary polynomial format to produce a received polynomial;
• means for converting the received polynomial into a plurality of binary error identifying polynomials;
• means for recursively processing the plurality of binary error identifying polynomials to produce a plurality of error identifying values;
• means for processing the plurality of error identifying values to produce an error locator polynomial that represents errors in the received polynomial;
• means for evaluating the error locator polynomial to identify the bit location of the error in the BCH encoded signal;
• and
• means for correcting the BCH encoded signal based on the bit location of the error.

An apparatus for decoding a BCH encoded signal, the apparatus comprises:

• means for receiving the BCH encoded signal in a binary polynomial format to produce a received polynomial;
• means for converting the received polynomial into a plurality of binary error identifying polynomials;
• for each of the plurality of binary error identifying polynomials having an odd index, means for dividing the received polynomial by a corresponding one of a plurality of minimum polynomials to obtain a quotient polynomial and a remainder polynomial during a given time interval, wherein the remainder polynomial represents one of the plurality of binary error identifying polynomials;
• means for recursively processing the plurality of remainder polynomials to produce a plurality of odd indexed syndrome components of a plurality of syndrome values;
• means for squaring each of the plurality of odd indexed syndrome components to produce a plurality of even indexed syndrome components of the plurality of syndrome values;
• means for processing the plurality of syndrome values to produce an error locator polynomial that represents errors in the received polynomial;
• means for evaluating the error locator polynomial to identify the bit location of the error in the BCH encoded signal;
• and
• means for correcting the BCH encoded signal based on the bit location of the error.

A method for pipelined decoding a BCH encoded signal, the method comprises:

• during a first interval of pipelined BCH decoding:
• receiving a first plurality of BCH encoded signals;
• determining, in parallel, at least first partial syndrome values for each of the first plurality of BCH encoded signals;
• during a second interval of the pipelined BCH decoding:
• receiving a second plurality of BCH encoded signals;
• determining, in parallel, at least second partial syndrome values for each of the second plurality of BCH encoded signals;
• determining, in serial, a first error locator polynomial for each of the first plurality of BCH encoded signals based on the corresponding at least first partial syndrome values;
• during a third interval of the pipelined BCH decoding:
• receiving a third plurality of BCH encoded signals;
• determining, in parallel, at least third partial syndrome values for each of the third plurality of BCH encoded signals;
• determining, in serial, a second error locator polynomial for each of the second plurality of BCH encoded signals based on the corresponding at least second partial syndrome values;
• and
• determining, in parallel, error location for each of the first plurality of BCH encoded signals based on the first error locator polynomials for each of the first plurality of BCH encoded signals.

An apparatus for pipelined decoding a BCH encoded signal, the apparatus comprises:

• processing module;
• and
• memory operably coupled to the processing module, wherein the memory includes operational instructions that cause the processing module to:
• during a first interval of pipelined BCH decoding:
• receive a first plurality of BCH encoded signals;
• determine, in parallel, at least first partial syndrome values for each of the first plurality of BCH encoded signals;
• during a second interval of the pipelined BCH decoding:
• receive a second plurality of BCH encoded signals;
• determine, in parallel, at least second partial syndrome values for each of the second plurality of BCH encoded signals;
• determine, in serial, a first error locator polynomial for each of the first plurality of BCH encoded signals based on the corresponding at least first partial syndrome values;
• during a third interval of the pipelined BCH decoding:
• receive a third plurality of BCH encoded signals;
• determine, in parallel, at least third partial syndrome values for each of the third plurality of BCH encoded signals;
• determine, in serial, a second error locator polynomial for each of the second plurality of BCH encoded signals based on the corresponding at least second partial syndrome values;
• and
• determine, in parallel, error location for each of the first plurality of BCH encoded signals based on the first error locator polynomials for each of the first plurality of BCH encoded signals.