Anexponential-Golomb code (or justExp-Golomb code) is a type ofuniversal code. To encode anynonnegative integerx using the exp-Golomb code:

1. Write downx+1 in binary
2. Count the bits written, subtract one, and write that number of starting zero bits preceding the previous bit string.

The first few values of the code are:

 0 ⇒ 1 ⇒ 1 1 ⇒ 10 ⇒ 010 2 ⇒ 11 ⇒ 011 3 ⇒ 100 ⇒ 00100 4 ⇒ 101 ⇒ 00101 5 ⇒ 110 ⇒ 00110 6 ⇒ 111 ⇒ 00111 7 ⇒ 1000 ⇒ 0001000 8 ⇒ 1001 ⇒ 0001001...[1]

In the above examples, consider the case 3. For 3, x+1 = 3 + 1 = 4. 4 in binary is '100'. '100' has 3 bits, and 3-1 = 2. Hence add 2 zeros before '100', which is '00100'

Similarly, consider 8. '8 + 1' in binary is '1001'. '1001' has 4 bits, and 4-1 is 3. Hence add 3 zeros before 1001, which is '0001001'.

This is identical to theElias gamma code ofx+1, allowing it to encode 0.^[2]

Exp-Golomb coding is used in theH.264/MPEG-4 AVC and H.265High Efficiency Video Coding video compression standards, in which there is also a variation for the coding of signed numbers by assigning the value 0 to the binary codeword '0' and assigning subsequent codewords to input values of increasing magnitude (and alternating sign, if the field can contain a negative number):

 0 ⇒ 0 ⇒ 1 ⇒ 1 1 ⇒ 1 ⇒ 10 ⇒ 010−1 ⇒ 2 ⇒ 11 ⇒ 011 2 ⇒ 3 ⇒ 100 ⇒ 00100−2 ⇒ 4 ⇒ 101 ⇒ 00101 3 ⇒ 5 ⇒ 110 ⇒ 00110−3 ⇒ 6 ⇒ 111 ⇒ 00111 4 ⇒ 7 ⇒ 1000 ⇒ 0001000−4 ⇒ 8 ⇒ 1001 ⇒ 0001001...[1]

In other words, a non-positive integerx≤0 is mapped to an even integer −2x, while a positive integerx>0 is mapped to an odd integer 2x−1.

Exp-Golomb coding is also used in theDirac video codec.^[3]

To encode larger numbers in fewer bits (at the expense of using more bits to encode smaller numbers), this can be generalized using anonnegative integer parameter  k. To encode a nonnegative integerx in an order-k exp-Golomb code:

1. Encode ⌊x/2^k⌋ using order-0 exp-Golomb code described above, then
2. Encodex mod 2^k in binary with k bits

An equivalent way of expressing this is:

1. Encodex+2^k−1 using the order-0 exp-Golomb code (i.e. encodex+2^k using the Elias gamma code), then
2. Deletek leading zero bits from the encoding result

• Elias gamma (γ) coding
• Elias delta (δ) coding
• Elias omega (ω) coding
• Universal code

• Entropy coding
• Numeral systems
• Data compression

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