B.S.T.J. Briefs: An Improved Error Bound for Gaussian Channels

The problem considered here is that of coding for the time-discrete amplitude-continuous memoryless channel with additive Gaussian noise, the code words lying on the surface of an n-dimensional hypersphere with center at the origin and radius y/ nP. We define a code as a set of .1/ real n-vectors x = (.Vi, .r 2 , · · · , x,,) satisfying the ("energy") constraint, 11 E-V = nP. (1) k= 1 The transmission rate R is defined by J/ = e', so that It = (1 Jn) In M.