An asymptotic lower bound on the rates of two-level binary codes with unequal error protection is presented. The bound is based on a class of codes that are constructive in the sense that the description complexity is polynomial in the codeword length. In some cases, the bound exceeds an upper bound for linear codes, proving the existence of constructive nonlinear UEP codes that are better than any linear codes.

The parameters of some binary nonlinear two-level unequal error-protection (UEP) codes are evaluated and compared with nonexistence bounds for linear UEP codes. The major points is that for UEP codes linearity is an essential restriction. The results demonstrate that at least in certain cases nonlinear codes perform better than linear ones. This is in contrast to the situation for ordinary codes, when in most cases the best possible result can be obtained even with the restriction of linearity.>