Forward error correcting code encoder and decoder method and apparatus

A method, implemented in a device having (i) a first plurality of processing stages coupled in series and (ii) a second plurality of processing stages coupled in series, of generating redundant symbols of a codeword from original symbols according to an error correcting code, wherein the original symbols include a first subset of original symbols and a second subset of original symbols, the method comprising:

• iteratively calculating, in the first plurality of processing stages, a first subset of redundant symbols of the codeword, wherein the first subset of redundant symbols is iteratively calculated as a function of (i) the first subset of original symbols, (ii) the second subset of original symbols, (iii) a sequence of outputs of a last processing stage of the first plurality of processing stages, and (iv) a sequence of outputs of a last processing stage of the second plurality of processing stages;
• and
• iteratively calculating, in the second plurality of processing stages, a second subset of redundant symbols of the codeword, wherein the second subset of redundant symbols is interatively calculated as a function of (i) the first subset of original symbols, (ii) the second subset of original symbols, (iii) the sequence of outputs of the last processing stage of the first plurality of processing stages, and (iv) the sequence of outputs of the last processing stage of the second plurality of processing stages.

A method, implemented in a device having a plurality of processing stages, of detecting and correcting errors in a received codeword, the received codeword including (i) a first plurality of codeword symbols and (ii) a second plurality of codeword symbols, the method comprising:

• generating, in each of the plurality of processing stages and over a plurality of iterations, a respective syndrome value of a plurality of syndrome values, wherein generating the respective syndrome value includes processing, during each of the plurality of iterations, (i) a symbol, of the first plurality of codeword symbols, corresponding to the respective one of the plurality of iterations and (ii) a symbol, of the second plurality of codeword symbols, corresponding to the respective one of the plurality of iterations;
• calculating, at the device, an error locator polynomial for the received codeword based on the plurality of syndrome values;
• calculating, at the device, one or more error values for one or more codeword symbols in the received codeword based on the error locator polynomial;
• and
• correcting, at the device, the received codeword using the one or more error values for the one or more codeword symbols in the received codeword.