Python – Golomb Encoding for b=2n and b!=2n

The Golomb coding is a form of parameterized coding in which integers to be coded are stored as values relative to a constant b Coding:- A positive number x is spoken to in two sections:

• The initial segment is an unary portrayal of q+1, where q is the remainder floor((x/b)), and
• The subsequent part is an extraordinary double portrayal of the leftover portion r = x-qb. Note that there are b potential leftovers.

For instance, if b = 3, the potential remnants will be 0, 1 and 2. To spare space, compose the initial couple of remnants utilizing floor(log(b, 2)) bits and the rest utilizing ceil(log(b, 2)) bits. We should do so with the end goal that the decoder knows at the point when floor(log(b, 2)) bits are utilized and when ceil(log(b, 2)) bits are utilized Examples:

Input  : N = 37, M = 11 
Output : 0001100

Code : Python program to implement Golomb Encoding

Python3

# Python programming for Golomb Encoding
import math

# taking input for N and  M where
# M == 2 ^ n or M != 2 ^ n
N = 37
M = 11

# for finding the value of preceding
# number of zeros by dividing N by M
q = N//M
# for computing the remainder of N by M
r = N % M

# appending that many numbers of zeros in
# starting of the encoded code initially
quo ='0'*q+'1'

# for computing the value of b ie floor of
# log(M) base 2 which will be used for computing value of k
b = math.floor(math.log2(M))
k = 2**(b + 1)-M
# upon comparing the value of remainder with the
# value of k if less we convert remainder r to
# binary and add the value from # index 2 because
# at index 0, 1 "0b" is present
if r < k:
    rem = bin(r)[2:]
    l = len(rem)

# upon the calculating value of rem if it is less than
# computed value of b we add b-1 number of zeros in
# preceding of the # remainder
    if l<b:
        rem = '0'*(b-l)+rem
else:
# we convert remainder r to binary and add the
# value from index 2 because at index 0, 1 "0b" is present
    rem = bin(r + k)[2:]
    l = len(rem)
# upon calculating value of rem if it is less than
# computed value of b we add b-1 number of zeros in
# preceding of the # remainder
    if l<b + 1:
        rem = '0'*(b + 1-l)+rem
golomb_code = quo + rem
print("The golomb code encoding for x = {} and b = {} is {}".
      format(N, M, golomb_code))

Output : 

The golomb code encoding for x = 37 and b = 11 is 0001100