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We study a form of unequal error protection that we term "unequal messageprotection" (UMP). The message set of a UMP code is a union of $m$ disjointmessage classes. Each class has its own error protection requirement, with someclasses needing better error protection than others. We analyze the tradeoffbetween rates of message classes and the levels of error protection of thesecodes. We demonstrate that there is a clear performance loss compared tohomogeneous (classical) codes with equivalent parameters. This is in sharpcontrast to previous literature that considers UMP codes. To obtain our resultswe generalize finite block length achievability and converse bounds due toPolyanskiy-Poor-Verd\'{u}. We evaluate our bounds for the binary symmetric andbinary erasure channels, and analyze the asymptotic characteristic of thebounds in the fixed error and moderate deviations regimes. In addition, weconsider two questions related to the practical construction of UMP codes.First, we study a "header" construction that prefixes the message class into aheader followed by data protection using a standard homogeneous code. We showthat, in general, this construction is not optimal at finite block lengths. Wefurther demonstrate that our main UMP achievability bound can be obtained usingcoset codes, which suggests a path to implementation of tractable UMP codes.

Unequal Message Protection: Asymptotic and Non-Asymptotic Tradeoffs