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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...
We present an improved sphere-packing (ISP) bound for finite-length error-correcting codes whose transmission takes place over symmetric memoryless channels, and the codes are decoded by an arbitrary list decoder. Some applications of the ISP bound are also exemplified. Its tightness under maximum-likelihood (ML) decoding is studied by comparing the ISP bound to previously reported upper and lower...
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