On the construction of efficient multilevel coded modulations

The methodology of multi-stage iterative decoding with exchange of soft information has previously been applied to a wide range of error-controlling codes with remarkable success, including parallel/serial concatenated convolutional/block codes (Berrou et al., 1993) and generalized concatenated convolutional codes (Cheng). A theoretical explanation of this decoding mechanism has been proposed (MacKay et al.) via the belief propagation algorithm (BPA) (Pearl 1988). It is shown that, by representing a turbo code with a Bayesian belief network, the application of BPA directly leads to the turbo decoding algorithm. In fact, it is argued that the decoding algorithms for all the aforementioned variations of the turbo coding construction as well as a wide range of low-density parity check codes can be explained by this principle. The author goes on to discuss low density generator matrix codes.