A method and apparatus are disclosed for MAP decoding of signals encoded using
error correction codes to make maximum probability decisions about each transmitted
bit. A MAP decoding algorithm is disclosed that exploits properties of Reed-Muller
error correction codes that use q-ary block codes to provide a decoding algorithm
having a complexity that is proportional to n logq n for Reed-Muller
codes. The disclosed MAP decoding algorithm employs two matrices D and {overscore
(D)} to represent the code set and has an overall complexity that is exponential
for a general code set. For Reed-Muller codes, the disclosed MAP decoding algorithm
employs matrices Bi and {overscore (Bi)} that are sparse
matrices (i.e., contain many zero entries), thereby reducing the number of required
operations and yielding a complexity that is proportional to n logq n.
In addition, the disclosed MAP decoding algorithm permits faster decoding by permitting
a parallel implementation having a critical path length that is proportional to
2 logq n for Reed-Muller codes.
