Balanced Codes and Nonequiprobable Signaling

The problem of shaping signal constellations that are designed for the Gaussian channel is considered. The signal constellation consists of all points from some translate of a lattice A, that lie within a region $. The signal constellation is partitioned into T annular subconstellations Q0, • • •, 0r_! by scaling the region 0L. Signal points in the same subconstellation are used equiprobably, and a shaping code selects region fi, with frequency fi. 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. It is described how balanced binary codes constructed by Knuth can be used to avoid a data rate that is probabilistic. The basic idea is that if symbols 0 and 1 represent constellations of unequal size, and if all shaping codewords have equally many 0’s and l’s, then the data rate will be deterministic. © 1992 IEEE

Duke Scholars

Author Robert Calderbank Computer Science