Balanced Codes and Non-Equiprobable Signaling.

We consider the problem of shaping signal constellations that are designed for the Gaussian channel. The signal constellation consists of all points from some translate of a lattice LAMBDA, that line within a region R. The signal constellation is partitioned into T annular subconstellations OMEGA sub O, ..., OMEGA sub (T-1) by scaling the region R. Signal points in the same subconstellation are used equiprobably, and a shaping code selects region OMEGA sub i with frequency f sub i. If the signal constellation is partitioned into annular subconstellations of unequal size, then absent some cleverness, the transmission rate will vary with the choice of codeword in the shaping code, and it will be necessary to queue the data in buffers. We describe how balanced binary codes constructed by Knuth can be used to avoid a data rate that is probablistic.