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Suppose that more than two dimensions are available for our

Qusetion: Suppose that more than two dimensions are available for our alphabet. Consider an alphabet where the symbols are vertices of an M dimensional hypercube, shown for M = 3 in the following figure

Assume that all the symbols are equally likely and the noise in each dimension is independent with variance σ².

(a) What are the decision regions?

(b) What is the probability of error as a function of M and the minimum distance d between points in the signal constellation.

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