Iterative equalization using non-linear models in a soft-input soft-output trellis

A method for trellis-based sequence estimation of a satellite communication signal using the algorithm by Bahl, Cocke, Jelinek, and Raviv (BCJR), comprising:

• generating a trellis using a computer;
• using the computer, generating one or more predicted symbols using a set of non-linear modeling coefficients corresponding to a first non-linear model;
• using the computer, computing and saving two or more branch metrics for a current time increment using a priori log-likelihood ratio (LLR) information for one or more coded bits, a channel observation for the current time increment, and one or more of the one or more predicted symbols;
• if alpha forward recursion has not yet completed, using the computer, generating two or more alpha forward recursion state metrics for the current time increment by, using a second non-linear model, applying an add compare select (ACS) algorithm to the two or more branch metrics for the current time increment and to two or more alpha forward recursion state metrics for a last previous time increment;
• if beta backward recursion has not yet completed, using the computer, generating two or more beta backward recursion state metrics for the current time increment by, using a third non-linear model, applying an ACS algorithm to the two or more branch metrics for the current time increment and to two or more beta backward recursion state metrics for the last previous time increment;
• if sigma forward recursion has not yet completed, using the computer, generating two or more sigma forward recursion state metrics for the current time increment using the two or more branch metrics for the current time increment, the two or more alpha state metrics for the current time increment, and the two or more beta backward recursion state metrics for the current time increment, to estimate a sequence for the trellis;
• using the computer, generating extrinsic information comprising a difference of a posteriori LLR information for the one or more coded bits and the a priori LLR information;
• using a decoder, decoding the satellite communication signal by computing and feeding back the a priori LLR information;
• and
• using the computer, calculating the a posteriori LLR information.