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Conventional formulations of communication problem have the tacit assumption that any error event is equally undesirable as any other error event. The multi-layer bit-wise unequal error protection problem is considered for variable length block codes with feedback. Inner and outer bounds are derived for achievable performance for finite expected decoding time. These bounds completely characterize the achievable volume for rate vector-error exponent vector pairs. The single message message-wise unequal error protection problem is also solved as a necessary step on the way.
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