On the optimality of multilevel coding and multistage decoding

Multilevel coding (MLC) is a method for constructing error correcting codes from codes with smaller alphabets. Using maximum likelihood decoding (MLD) or multistage decoding (MSD) they can be used for communication over channels with larger alphabets. It is widely known that MLC with MSD may achieve the channel capacity for many channels. Such results are based the chain rule of the mutual information. In this work we formalize the conditions in which capacity of any discrete memoryless channel (DMC) is achieved by multilevel codes with MLC and MSD. We continue by analyzing the error exponent of the MLC-MSD scheme for DMCs. It appears that even in cases where MLC with either MLD or MSD achieve the channel capacity, the error exponent may be lower than the error exponent achieved by using general codes.