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Elias Gamma Decoding in Python

  • Difficulty Level : Expert
  • Last Updated : 28 Nov, 2021

The Elias gamma code is a universal code that is used to encode a sequence of positive integers. It is developed by Peter Elias. It is most useful when the upper-bound of integers cannot be determined beforehand.

Formula:

Elias Gamma Coding=Unary(1+floor(log2(x)))+Binary representation of ‘x’ without MSB

Example: Let’s consider an example where we want to decode 0001001,

Apply Step 1:
Count the number of '0's from MSB until you reach the first '1' and store the count in K.
In our example(0001001) K=3 

Apply Step 2:
Read 3 more bits including the first '1'=1001

Apply Step 3:
Convert the final binary into integer which gives us the original number.
Decimal(1001)=9

Stepwise Implementation

Step 1: Count the number of ‘0’s from MSB until you reach the first ‘1’ and store the count in K.

Python3




# define the function
def Elias_Gamma_Decoding(x):
    
    # convert to list
    x = list(x)
      
    # initialize k to 0
    K = 0
    while True:
        
        # check if k is not 0 in through
        # list index
        if not x[K] == '0':
            break
          
        # increment k value
        K = K + 1

Step 2: Consider that ‘1’ as the first digit and read ‘K’ more bits from the current ‘1’

Python3




x = x[K:2*K+1# Reading K more bits from '1'

Step 3: Convert the final binary into an integer which gives us the original number.

Python3




# Converting binary to integer
for i in range(len(x)):
    if x[i] == '1':
        n = n+math.pow(2, i)
return int(n)

Below is the complete implementation of the above approach.

Python3




# import the math module
import math
  
# function
def Elias_Gamma_Decoding(x):
    x = list(x)
    K = 0
    while True:
        if not x[K] == '0':
            break
        K = K + 1
      
    # Reading K more bits from '1'
    x = x[K:2*K+1]
  
    n = 0
    x.reverse()
      
    # Converting binary to integer
    for i in range(len(x)):
        if x[i] == '1':
            n = n+math.pow(2, i)
    return int(n)
  
  
# value input
x = '0001001'
  
# call the function
print(Elias_Gamma_Decoding(x))

Output:

9


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