On reliability functions for single-message unequal error protection

Single-message unequal error protection (UEP) is a channel coding scheme that protects one special message differently from other (regular) messages. This induces three different types of errors in the system: 1) miss (where we decode the special codeword as a regular codeword), 2) false alarm (where we decode a regular codeword as the special codeword), and 3) decoding error (where we decode a regular codeword to another regular codeword). In this paper, we investigate the fundamental limits of single-message UEP, in the context of discrete memoryless channels (DMCs) without feedback. Similar to Borade et al., we use error exponents as the performance metric, and discuss maximizing the miss error exponent and the false alarm error exponent, respectively. We provide a new converse proof for the miss reliability function, i.e., the optimal miss error exponent as a function of communication rate, and extend the inner and outer bound results for the false alarm reliability function in Borade et al. from rates close to capacity to all rates up to capacity.