Polynomial approximation techniques for probabilistic amplitude shaping

An apparatus for wireless communication at a transmitter device, comprising:

• a memory;
• and
• one or more processors, coupled to the memory, configured to:
• obtain a plurality of information bits for a probabilistic shaping scheme, the probabilistic shaping scheme being associated with an energy threshold;
• form, as part of the probabilistic shaping scheme, polynomial approximations of a plurality of approximation factors;
• obtain, using the polynomial approximations of the plurality of approximation factors, an approximation of a logarithm of a cumulative sequence quantity, the logarithm of the cumulative sequence quantity being associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy;
• perform an exponentiation operation on the approximation of the logarithm of the cumulative sequence quantity, thereby obtaining an approximation of the cumulative sequence quantity;
• encode, as part of the probabilistic shaping scheme, the plurality of information bits to obtain a symbol sequence based at least in part on the approximation of the cumulative sequence quantity, the symbol sequence having a length equal to a second sequence length and an energy less than or equal to the energy threshold, wherein each symbol of the symbol sequence belongs to a second alphabet having a second alphabet size;
• and
• transmit a message to one or more receiver devices based at least in part on the symbol sequence.