Levenshtein coding


Levenshtein coding is a universal code encoding the non-negative integers developed by Vladimir Levenshtein.

Encoding

The code of zero is "0"; to code a positive number:
  1. Initialize the step count variable C to 1.
  2. Write the binary representation of the number without the leading "1" to the beginning of the code.
  3. Let M be the number of bits written in step 2.
  4. If M is not 0, increment C, repeat from step 2 with M as the new number.
  5. Write C "1" bits and a "0" to the beginning of the code.
The code begins:
To decode a Levenshtein-coded integer:
  1. Count the number of "1" bits until a "0" is encountered.
  2. If the count is zero, the value is zero, otherwise
  3. Discard the "1" bits just counted and the first "0" encountered
  4. Start with a variable N, set it to a value of 1 and repeat count minus 1 times:
  5. Read N bits, prepend "1", assign the resulting value to N
The Levenshtein code of a positive integer is always one bit longer than the Elias omega code of that integer. However, there is a Levenshtein code for zero, whereas Elias omega coding would require the numbers to be shifted so that a zero is represented by the code for one instead.

Example code

Encoding


void levenshteinEncode

Decoding


void levenshteinDecode