Elias ω coding or Elias omega coding is a universal code encoding the positive integers developed by Peter Elias. Like Elias gamma coding and Elias delta coding, it works by prefixing the positive integer with a representation of its order of magnitude in a universal code. Unlike those other two codes, however, Elias omega recursively encodes that prefix; thus, they are sometimes known as recursive Elias codes.
Omega coding is used in applications where the largest encoded value is not known ahead of time, or to compress data in which small values are much more frequent than large values.
To encode a positive integer N:
Place a "0" at the end of the code.
If N = 1, stop; encoding is complete.
Prepend the binary representation of N to the beginning of the code. This will be at least two bits, the first bit of which is a 1.
Let N equal the number of bits just prepended, minus one.
Return to Step 2 to prepend the encoding of the new N.
To decode an Elias omega-encoded positive integer:
Start with a variable N, set to a value of 1.
If the next bit is a "0" then stop. The decoded number is N.
If the next bit is a "1" then read it plus N more bits, and use that binary number as the new value of N. Go back to Step 2.
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