Agile data rates via arithmetic base conversion

An arithmetic base converter provides highly flexible modem operation. The arithmetic base conversion is unconstrained by bit rate and symbol rate combinations. It converts a desired fractional number of bits per symbol to the appropriate arithmetic base. Fractional bit rate modulation allows high speed modems to operate in any bandwidth and at any data rate to optimize the channel bandwidth and signal-to-noise ratio. The symbol rate matches the optimum bandwidth of the channel. The number of points in the constellation subset is equal to the arithmetic base. The signal constellation is power indexed such that constellation power and size increase monotonically with data rate. This arrangement allows one constellation table to accommodate variable data rates with optimum packing for minimum power in all cases and a circular constellation shape to minimize peak factor