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 (and remove them from the encoded integer), 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

Decoding

See also

• Elias omega coding
• Iterated logarithm