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The probability of error for the transmission of one of -orthogonal, equally likely, equal-energy signals over the white Gaussian noise channel is known. For large values of it is shown that this result is asymptotically equivalent to the error probability for the same signal set transmitted over a different channel, termed here the generalized incoherent channel of order . For this channel is identical to the phase incoherent channel. This problem, for larger values of , also arises in a number of other applications, some of which are given.