Method and apparatus for weighted majority decoding of FEC codes using soft detection

A method of weighted majority decoding of code symbol signals included in a forward error correcting (FEC) code, said code symbol signals including information symbol signals representing information symbols having at least first and second code values and parity symbol signals representing parity symbols generated from selected combinations of said information symbols, said method comprising the steps of:

• receiving information symbol signals representing the code values of said information symbols;
• receiving parity symbol signals representing the values of said parity symbols;
• soft detecting said information symbol signals to detect the voltage of each information symbol signal;
• generating a code value signal indicating the code value represented by each said information symbol signal;
• generating an information symbol reliability signal representing the reliability of each said code value signal;
• soft detecting said parity symbol signals to detect the voltage of each parity symbol signal;
• generating a parity value signal indicating the value represented by each said parity symbol signal;
• generating a parity symbol reliability signal representing the reliability of each said parity value signal;
• generating a first estimate of the code value of a particular information symbol from the code value signal corresponding to that symbol;
• combining m selected ones of said code and parity value signals to obtain at least one further estimate of the code value of said particular information symbol;
• assigning to said first estimate an estimate weighting factor in accordance with the information symbol reliability signal corresponding to the self-detected information symbol signal for said particular information symbol;
• determining for said at least one further estimate an estimate weighting factor derived from the reliability signals of the I least reliable code and parity value signals which were combined to obtain said at least one further estimate, where I is an integer greater than 1 and less than m;
• combining corresponding estimate weighting factors and code value estimates to obtain weighted estimates;
• combining said weighted estimates to obtain a combined weighted estimate;
• and
• providing a decoded symbol in accordance with the value of said combined weighted estimate.

A method of weighted majority decoding of code symbol signals included in a forward error correcting (FEC) code, said code symbol signals including information symbol signals representing information symbols having at least first and second code values and parity symbol signals representing parity symbols generated from selected combinations of said information symbols, said method comprising the steps of:

• receiving information symbol signals representing the code values of said information symbols;
• receiving parity symbol signals representing the values of said parity symbols;
• soft detecting said information symbol signals to detect the voltage of each information symbol signal;
• generating a code value signal indicating the code value represented by each said information symbol signal;
• assigning to each code value signal a number of demerits corresponding to the reliability of the code value represented by each said code value signal;
• soft detecting said parity symbol signals to detect the voltage of each said parity symbol signal;
• generating a parity value signal corresponding to the value of each parity symbol signal;
• assigning to each parity symbol signal a number of demerits corresponding to the reliability of the parity value represented by said parity symbol signal;
• combining selected ones of said code and parity value signals to obtain a plurality of estimates of the code value of a particular information symbol;
• combining the demerits assigned to each of the code and parity value signals used to obtain each estimate in order to obtain a combined demerit value for each said estimate;
• assigning to each said estimate an estimate weighting factor in accordance with said combined demerit value;
• combining corresponding estimate weighting factors and code value estimates to obtain weighted estimates;
• combining said weighted estimates to obtain a combined weighted estimate;
• and
• providing a decoded symbol in accordance with the value of said combined weighted estimate.

A method of weighted majority decoding of a forward error correcting (FEC) code, said code comprising code symbol signals including information symbol signals representing information symbols having at least first and second code values and parity symbol signals representing parity symbols generated from selected combinations of said information symbols, said method comprising the steps of:

• soft-detecting said information and parity symbol signals and generating for each of said soft-detected signals a multi-bit signal having one bit representing the value of the detected symbol signal and a plurality of remaining bits representing the reliability of said symbol value;
• combining said one bits of selected ones of said multibit signals to obtain a plurality of estimates of the code value of a particular information symbol;
• determining an estimate weighting factor for each said estimate in accordance with the least reliable code value used in obtaining said estimate, said determining step comprising the steps of combining corresponding ones of said remaining bits for each symbol in respective AND gates, the combined outputs of said AND gates being the equivalent of the remaining bits of the least reliable term involved in said estimate, and assigning to each said estimate a weighting factor corresponding to the combined outputs of said AND gates;
• combining the estimate weighting factors and corresponding code value estimates to obtain a plurality of weighted estimates of said particular symbol;
• combining said weighted estimates to obtain a combined weighted estimate;
• and
• providing a decoded symbol in accordance with the value of said combined weighted estimate.

A method of generating a forward error correcting (FEC) majority logic decodable code from a series of information bits, said code comprising a series of output code symbol signal sets, said code being a rate .rho.=k/n code wherein each output code symbol set includes k information symbols and (n-k) parity symbols where n and k are positive integers and n>k, said method comprising the steps of:

• providing said k information symbols to k respective information symbol shift registers;
• coupling selected stages of each of said k information symbol shift registers as a first set of inputs to each of (n-k) modulo-2 adders, each of which modulo-2 adders combine its respective first set of inputs with a second set of inputs and provides a parity symbol output;
• and
• providing the parity symbol output from each adder as an input to a corresponding one of (n-k) parity symbol shift registers, selected stages of said parity symbol shift registers being provided as said second set of inputs to corresponding modulo-2 adders, the inputs to said information and parity symbol shift registers constituting an output code symbol set.

In a method of decoding a majority logic decodable code, said method being of the type including receiving at a first decoder information and parity symbol signals representing information and parity symbols in said code, regenerating parity symbol estimates from said received information symbol signals, comparing said received parity symbols and regenerated parity symbol estimates to generate a parity check syndrome, and passing or correcting said received information symbol in accordance with a majority logic decision on said parity check syndrome, the improvement comprising:

• receiving said detected information symbols at a second decoder;
• generating a second set of parity symbol estimates from said decoded information symbols in a second encoder replica;
• comparing said second set of parity symbol estimates to said received parity symbols in order to generate a second parity check syndrome;
• combining said decoded information symbols with selected stages of said second parity check syndrome in order to generate a plurality of estimates of each said information symbol;
• and
• passing or correcting said detected information symbol in accordance with a majority logic decision on said plurality of estimates and on said detected information symbol.

In a method of decoding majority logic decodable codes, said method being of the type including the steps of receiving and detecting at a first decoder information and parity symbol signals, regenerating parity symbol estimates from said received information symbol signals in an encoder replica, comparing said received parity symbol signals and regenerated parity symbol estimates to generate a parity check syndrome, correcting or passing said detected information symbol as a decoded value output in accordance with a majority polling of said parity check syndrome, and updating the contents of said parity check syndrome in accordance with said majority decision, the improvement comprising:

• receiving said detected information symbols at a second decoder;
• receiving said decoded information symbols at said second decoder;
• receiving said updated parity check syndrome at said second decoder;
• combining said decoded information symbols and said updated parity check syndrome in order to obtain a plurality of estimates of said information symbol;
• and
• passing or correcting said detected information symbol in accordance with a majority logic decision on said information symbol and said plurality of estimates.