We investigate the asymptotic (in blocklength) 
tradeoffs between rate and minimum distance, for codes that 
provide unequal error protection (UEP). Two notions of UEP are 
analyzed: bit-wise, where a subset of bits is special and needs more 
protection, and message-wise, where a subset of the message-set 
is special. Both notions are analyzed for two cases: binary, and 
large-alphabet. 

In message-wise UEP for the binary channel alphabet, it 
turns out that the special messages and ordinary messages can 
simultaneously achieve the Gilbert-Varshamov bound at their 
respective rates. Similar “successive refinement” of the Singleton 
bound is shown to hold for large non-binary alphabets. We also 
analyze the situation when there is only one special message. 
In bit-wise UEP, it is shown that when the ordinary bits are 
achieving the Singleton bound, even a single special bit cannot 
achieve any larger distance. For the binary case, an upper bound 
is provided on the protection of the single special bit. These 
coding theoretic limits in terms of Hamming distances are close 
analogues of the information theoretic limits  in terms of 
error exponents by Borade et al.