Data compression : from positive integers to signed integers

Basic 

We compressing integers, algorithms like Elias Gamma, are based on strictly positive integers. It is possible to also encode negative integer with a simple bijection

We want to encode X.   X can be zero, positive or negative, we will first transform X into a new (and positive) integer :

if X >=0 : f(X)= 2*X+1
if X <0 : f(X)= -2*X

Examples with gamma encoding

x=6

f(X) = 12 + 1 = 13
gamma(13) = 000 1101

x=-6

f(-6) = 12
gamma(12) = 000 1100

We can notice that the gamma codes of 6 and -6 are almost the same, only the last bit is different and give use the sign (usefull to decode)


x=5

f(X) = 10 + 1 = 11
gamma(11) = 000 1011

x=-5

f(-5) = 10
gamma(12) = 000 1010