Calculation of shell frequency distributions obtained with shell-mapping schemes

In order to calculate the transmit power in shell-mapping-based transmissio n schemes, the frequencies of the shells are required. In this corresponden ce, a simple but general method for the calculation of these frequencies is derived. The method has approximately the same complexity as the shell-map ping encoder. As an example, the method is shown in detail for the shell-ma pping scheme specified for the international telephone-line V.34 modem stan dard. Moreover, a very simple approximation is given which is tight for lar ge constellations.