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:
Initialize the step count variable C to 1. Write the binary representation of the number without the leading "1" to the beginning of the code. Let M be the number of bits written in step 2. If M is not 0, increment C, repeat from step 2 with M as the new number. Write C "1" bits and a "0" to the beginning of the code. The code begins:
To decode a Levenshtein-coded integer:
Count the number of "1" bits until a "0" is encountered. If the count is zero, the value is zero, otherwise Discard the "1" bits just counted and the first "0" encountered Start with a variable N, set it to a value of 1 and repeat count minus 1 times: 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
References