A new block shaping scheme

In traditional modems, constellation symbols are selected equiprobably, but the forthcoming V34 standard changes this situation by including a technique called shaping. Shaping increases the power efficiency of constellations by optimising the shape of the region bounding the signal set. In fact, a maximum gain of 1.53 dB can be achieved if the symbols are selected from a 2N-dimensional sphere instead of a 2N-dimensional cube (N→∞). Equivalently, this gain can be obtained by imposing a Gaussian probability distribution on an infinite 2-dimensional constellation. It can be shown that a finite constellation size does not impair the achievable gain, so 1.53 dB is a practical gain. One way of reaching this limit is by using variable-length prefix codes. This method imposes a variable data rate and leads to many problems. We describe a new constant rate shaping scheme. Our technique is most closely related to Forney´s trellis shaping, but where trellis shaping uses convolutional codes and a trellis decoder to impose a non-uniform distribution on a 2-dimensional constellation, we employ block codes