Python中的 Elias Gamma 解码

Elias gamma 代码是一种通用代码，用于对正整数序列进行编码。它是由彼得埃利亚斯开发的。当无法预先确定整数的上限时，它最有用。

公式：

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

示例：让我们考虑一个要解码 0001001 的示例，

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

逐步实施

第 1 步：从 MSB 计算“0”的数量，直到到达第一个“1”，并将计数存储在 K 中。

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

第 2 步：将“1”视为第一个数字，并从当前“1”中读取“K”位

Python3

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

第 3 步：将最终的二进制转换为整数，得到原始数字。

Python3

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

下面是上述方法的完整实现。

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))

输出：

9