A geometric treatment of the source encoding of a Gaussian random variable

This paper gives a geometric treatment of the source encoding of a Gaussian random variable for minimum mean-square error. The first section is expository, giving a geometric derivation of Shannon's classic result [1] which explicitly shows the steps in source encoding and the properties that a near optimum code must possess. The second section makes use of the geometric insight gained in the first section to bound the performance that can be obtained with a finite block length ofLrandom variables. It is shown that a code can be found whose performance approaches that of the rate distortion function as1/Lin mean-square error and(ln L)/Lin rate.