1. A method for combinatorial coding and decoding, the method comprising the steps of: receiving a vector comprising speech, audio, image, or video; receiving a value n based on a number of positions in the vector; receiving a value d based on a number of occupied positions within the vector; generating a value F′(n, d) based on a logarithmic approximation of the combinatorial function of F(n,d) and comprising generating a logarithmic approximation of a numerator of F(n,d) and generating a logarithmic approximation of a denominator by subtracting a combinatorial function Q′(d) from the numerator; and using the value F′(n, d) to code or decode the vector to produce coded or decoded speech, audio, image, or video.