指数哥伦布码

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指数哥伦布码是一种无损数据压缩技术，主要用于表示非负整数。该编码过程包括移除最低k位、加1、计算前导零数量并重组比特串。本文详细介绍了0阶和1阶指数哥伦布码的生成步骤，并通过实例解析了编码过程。了解这一编码方法对于理解数据压缩原理和实现具有重要意义。

指数哥伦布码（Exponential-Golomb coding）是一种无损数据压缩方法。

用来表示非负整数的k阶指数哥伦布码可用如下步骤生成：

将数字以二进制形式写出(B)，去掉最低的k个比特(D)，之后加1 (A = (B >> k) + 1)
计算A的比特个数(C)，将此数减一，即是需要增加的前导零个数(Z = C -1)
将第一步中去掉的最低k个比特位补回比特串尾部 (ExpG = Z个0 + A + D)

0阶指数哥伦布码如下所示：

  Step 1                         Step 2          Step 3

0 => B = 0   ,D = None ,A = 1    => C = 1 ,Z = 0 => 1

1 => B = 1   ,D = None ,A = 10   => C = 2 ,Z = 1 => 010

2 => B = 10  ,D = None ,A = 11   => C = 2 ,Z = 1 => 011

3 => B = 11  ,D = None ,A = 100  => C = 3 ,Z = 2 => 00100

4 => B = 100 ,D = None ,A = 101  => C = 3 ,Z = 2 => 00101

5 => B = 101 ,D = None ,A = 110  => C = 3 ,Z = 2 => 00110

6 => B = 110 ,D = None ,A = 111  => C = 3 ,Z = 2 => 00111

7 => B = 111 ,D = None ,A = 1000 => C = 4 ,Z = 3 => 0001000

8 => B = 1000,D = None ,A = 1001 => C = 4 ,Z = 3 => 0001001

以数字9为例， (1)2进制值B 为1001,因为K为0阶，去除0个比特，故D值为空，把B值加1 得到 A，值为 1010， (2)计算A的比特个数，得到C值为4，故减1后得到前导零Z ,值为3 (3)最后组合 Z + A + D之后，得到 000+1010 + 空，故Exp-G值为 0001010

1阶指数哥伦布码如下所示：

  Step 1                     Step 2          Step 3

0 => B = 0   ,D = 0 ,A = 1   => C = 1 ,Z = 0 => 10

1 => B = 1   ,D = 1 ,A = 1   => C = 1 ,Z = 0 => 11

2 => B = 10  ,D = 0 ,A = 10  => C = 2 ,Z = 1 => 0100

3 => B = 11  ,D = 1 ,A = 10  => C = 2 ,Z = 1 => 0101

4 => B = 100 ,D = 0 ,A = 11  => C = 2 ,Z = 1 => 0110

5 => B = 101 ,D = 1 ,A = 11  => C = 2 ,Z = 1 => 0111

6 => B = 110 ,D = 0 ,A = 100 => C = 3 ,Z = 2 => 001000

7 => B = 111 ,D = 1 ,A = 100 => C = 3 ,Z = 2 => 001001

8 => B = 1000,D = 0 ,A = 101 => C = 3 ,Z = 2 => 001010