1. A method for encoding integers for transmission via a bitstream, the method comprising: receiving, by a processor, a vector of integers used in a data compression codebook, the sum of the integers equaling a pulse sum; determining, by the processor, an initial expected magnitude for a first integer of the vector of integers, the initial expected magnitude being based on the pulse sum, a distribution parameter, and a value corresponding to a number of integers in the vector of integers; encoding, by the processor, an actual magnitude of the first integer based on the initial expected magnitude; adjusting, by the processor, the pulse sum using the encoded actual magnitude; reducing, by the processor, the value corresponding to the number of integers in the vector by one; and calculating, by the processor, expected magnitudes for each of the remaining integers in the vector recursively based on the distribution parameter, the adjusted pulse sum and the reduced value corresponding to the number of integers in the vector.