Look-ahead maximum likelihood sequence estimation decoder

A Nearest Neighbors Look-Ahead Maximum Likelihood Estimation Sequence (LA-MLSE) algorithm for decoding data in a digital communications system forms the following three vectors to decode data: (1) a vector of the encoder input bit signals A=A{k, k+1, k+2}, (2) a vector of the noise-free encoder channel output signals Y=Y{A(k), A(k+1), A(k+2)}; and (3) a vector of the received signals R=R(A(k), A(k+1), A(k+2)). If the distance between the received signal R and at least one of the channel output vectors which are of the form Y{1, A(k+1), A(k+2)} is shorter than the distance between the received signal R and the Nearest Neighbor of the signal Y{1, A(k+1), A(k+2)}, then A(k) is decoded as 1. In an All Neighbors Look-Ahead MLSE algorithm, A(k) is decoded as 1 only if the distance between the received signal R and at least one of the channel output vectors which are of the form Y{1, A(k+1), A(k+2)} is shorter than all the distances between signal R and each of the channel output vectors which are of the form Y{0, A(k+1), A(k+2)}. In a Nearest Neighbor Adjusted Depth Look-Ahead MLSE algorithm, if the distance obtained using the first two time indices, i.e. k and k+1, is greater than a minimum distance, the time index k+2 is omitted from the calculations, thereby reducing the amount of computations necessary to estimate the value of the encoder input data.