Consider vertices-of-a-hyper-cube signaling, for which the  

in which the coefficients α_ik are permuted through the values +1 and -1, E_s is the signal energy, and the Ï•_ks
are orthonormal. Thus, M = 2ⁿ, where n = log₂ M is an integer. For M = 8, n = 3, the signal points in signal space lie on the vertices of a cube in three-space. 

(a) Sketch the optimum partitioning of the observation space for M = 8.

(b) Show that for M = 8 the symbol error probability 

P_E = 1 - P(C)

where

(c) Show that for n arbitrary the probability of symbol error is 

P_E = 1 - P(C) 

where

Transcribed Image Text:

E, а Ф, (1), 0