A multilevel qpsk communications system transmits three

Question

A multilevel QPSK communications system transmits three bits every unit of time. For each possible sequence i_jk of three bits, one of eight symbols, {s₀₀₀,s₀₀₁,...,s₁₁₁}, is transmitted. When signal s_ijk is transmitted, the receiver output is

Where N is a Gaussian (0, σ²I) random vector The 2-dimensional signal vectors s₀₀₀,...,s₁₁₁ are

Let H_ijk denote the hypothesis that s_ijk was transmitted. The receiver output X = [X₁ X₂] is used to decide the acceptance sets {A₀₀₀,..., A₁₁₁}. If all eight symbols are equally likely, sketch the acceptance sets.