Ced. Sterian, The constellation-shaping algorithm using closed-form expressions for the number of ring combinations, IEEE COMMUN, 47(10), 1999, pp. 1462-1465
The V.34 high-speed modem combines a number of advanced techniques includin
g constellation shaping by shell mapping. This technique makes use of some
functions representing the number of ring combinations with a given cost. I
n this correspondence, closed-form expressions for these functions are give
n and used in the constellation shaping by the shell-mapping algorithm.