APPROACHING CAPACITY BY EQUIPROBABLE SIGNALING ON THE GAUSSIAN-CHANNEL

For the additive white Gaussian noise channel, there is a gap between the channel capacity and the highest achievable rate of equiprobable u niformly spaced one-dimensional signaling [3]. It is commonly believed that approaching channel capacity requires the constituent one-dimens ional signal points to have a Gaussian probability distribution. Here, it is shown that channel capacity can be achieved by equiprobable sig naling with geometrical, Gaussian-like signal sets. Construction of th ese signal constellations is explicitly given. This result implicates that it is possible to approach channel capacity without using any kin d of shaping codes.