Patent ID: 7454453

Claim:
A method for correlating an encoded data word (X 0 -X M−1 ) with encoding coefficients (C 0 -C M−1 ), wherein each of (X 0 -X M−1 ) is represented by one or more bits and each said coefficient is represented by one or more bits, wherein each said coefficient has k possible states, wherein M is greater than 1, comprising: (1) receiving the encoded data word (X 0 -X M−1 ); (2) multiplying X 0 with states C 0(0) through C 0(K−1) of said coefficient C 0 , thereby generating results X 0 C 0(0) through X 0 C 0(K−1) ; (3) repeating step (1) for data bits (X 1 -X M−1 ) and corresponding said coefficients (C 1 -C M−1 ), respectively; (4) grouping said results of steps (2) and (3) into N groups and summing combinations within each of said N groups, thereby generating a first layer of correlation results; (5) grouping the results of step (4) and summing combinations of results within each group to generate one or more additional layers of results, and repeating this process until a final layer of results includes a correlation output for states of the set of coefficients (C 0 -C M−1 ); (6) comparing magnitudes output of said correlation outputs, thereby identifying a most likely code encoded on said data word; and (7) outputting the most likely code.