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Question: Consider M vectors each a distance d min from the other vectors. Assume an ML detector will be used to distinguish between these vectors.

(a) Give an example for M = 3 of such a set of vectors where d_min is a Euclidean distance of J2.

(b) Give an example for M = 3 of such a set of vectors where d min is a Hamming distance of 2.

(c) Use the union bound to find an upper bound on the probability of error for your two examples, assuming additive white Gaussian noise for (a) and a BSC for (b). First give the bound assuming 81 is transmitted, then give the bound without this assumption.

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