Gaussian Golomb Codes

This paper tackles this problem by mapping the normal distribution into the geometric distribution before applying Golomb codes, which is optimal for geometric distributions. In our mapping, a pair of normally-distributed i.i.d. integers (say (x,y)) is concatenated and then mapped to one natural number z(x,y). The conditions that z shall satisfy are: min_x,y Z(x,y)=0, l(x,y)<l(a,b)=>z(x,y)<z(a,b) and z(x,y)=z(a,b)< => (x,y) = (a,b), where l(x,y) is an arbitrary distance measure between the origin and the grid point (x,y), such as the Euclidean norm. The mapping can be easily obtained using a computer program. In addition, if the upper- and lower- bounds of the source is known, pre-calculated mapping table can be stored in the memory because it is independent of source statistics. Of course, this table is not needed to be downloaded/transmitted. After this mapping, z is made geometrically-distributed and conventional Golomb codes can be efficiently applied.