1 Introduction

The H.264 / AVC standard specifies two types of entropy coding: Context-based Adaptive Binary Arithmetic Coding (CABAC) and Variable-Length Coding (VLC). The Variable-Length Coding scheme is described in this document.

2  Coded elements

Parameters that require to be encoded and transmitted include the following (Table 21).

Parameters to be encoded

Above the slice layer, syntax elements are encoded as fixed- or variable-length binary codes. At the slice layer and below, elements are coded using either variable-length codes (VLCs) or context-adaptive arithmetic coding (CABAC) depending on the entropy encoding mode.

3 Variable length coding (VLC)

When entropy_coding_mode is set to 0, residual block data is coded using a context-adaptive variable length coding (CAVLC) scheme and other variable-length coded units are coded using Exp-Golomb codes.

3.1 Exp-Golomb entropy coding

Exp-Golomb codes (Exponential Golomb codes) are variable length codes with a regular construction. Table 31 lists the first 9 codewords; it is clear from this table that the codewords progress in a logical order. Each codeword is constructed as follows:

[M zeros][1][INFO]

where INFO is an M-bit field carrying information. The first codeword has no leading zero or trailing INFO; codewords 1 and 2 have a single-bit INFO field; codewords 3-6 have a 2-bit INFO field; and so on. The length of each codeword is (2M+1) bits.

Each Exp-Golomb codeword can be constructed by the encoder based on its index code_num: M = ⎣log2(code_num+1)⎦

INFO = code_num + 1 – 2M

A codeword can be decoded as follows:

  1. Read in M leading zeros followed by 1.
  2. Read M-bit INFO field.
  3. code_num = 2M + INFO – 1

(For codeword 0, INFO and M are zero).


Exp-Golomb codewords

A parameter v to be encoded is mapped to code_num in one of 3 ways:

ue(v)   : Unsigned direct mapping, code_num = v. Used for macroblock type, reference frame index and others.

se(v)   : Signed mapping, used for motion vector difference, delta QP and others. v is mapped to

code_num as follows (Table 32).

code_num = 2|v| (v < 0)

code_num = 2|v| - 1             (v ≥ 0)

Table 32 Signed mapping se(v)

Signed mapping

me(v) : Mapped symbols; parameter v is mapped to code_num according to a table specified in the standard. This mapping is used for the coded_block_pattern parameter. Table 33 lists a small part of the table for Inter predicted macroblocks: coded_block_pattern indicates which 8x8 blocks in a macroblock contain non-zero coefficients.

Table 33 Part of coded_block_pattern table

Part of coded-block-pattern table

Each of these mappings (ue, se and me) is designed to produce short codewords for frequently-occurring values and longer codewords for less common parameter values. For example, macroblock type Pred_L0_16x16 (i.e. 16x16 prediction from a previous picture) is assigned code_num 0 because it occurs frequently whereas macroblock type Pred_8x8 (8x8 prediction from a previous picture) is assigned code_num 3 because it occurs less frequently. The commonly-occurring motion vector difference (MVD) value of 0 maps to code_num 0 whereas the less-common MVD = -3 maps to code_num

3.2 Context-based adaptive variable length coding (CAVLC)

This is the method used to encode residual, zig-zag ordered 4x4 (and 2x2) blocks of transform coefficients. CAVLC is designed to take advantage of several characteristics of quantized 4x4 blocks:

  1. After prediction, transformation and quantization, blocks are typically sparse (containing mostly zeros). CAVLC uses run-level coding to compactly represent strings of zeros.
  2. The highest non-zero coefficients after the zig-zag scan are often sequences of +/-1. CAVLC signals the number of high-frequency +/-1 coefficients (“Trailing 1s” or “T1s”) in a compact way.
  3. The number of non-zero coefficients in neighbouring blocks is correlated. The number of coefficients is encoded using a look-up table; the choice of look-up table depends on the number of non-zero coefficients in neighbouring blocks.
  4. The level (magnitude) of non-zero coefficients tends to be higher at the start of the reordered array (near the DC coefficient) and lower towards the higher frequencies. CAVLC takes advantage of this by adapting the choice of VLC look-up table for the “level” parameter depending on recently-coded level magnitudes.


CAVLC encoding of a block of transform coefficients proceeds as follows.


1.  Encode the number of coefficients and trailing ones (coeff_token).

The first VLC, coeff_token, encodes both the total number of non-zero coefficients (TotalCoeffs) and the number of trailing +/-1 values (T1). TotalCoeffs can be anything from 0 (no coefficients in the 4x4 block)1 to 16 (16 non-zero coefficients). T1 can be anything from 0 to 3; if there are more than 3 trailing +/-1s, only the last 3 are treated as “special cases” and any others are coded as normal coefficients.

There are 4 choices of look-up table to use for encoding coeff_token, described as Num-VLC0, Num-VLC1, Num-VLC2 and Num-FLC (3 variable-length code tables and a fixed-length code). The choice of table depends on the number of non-zero coefficients in upper and left-hand previously coded blocks Nu and NL. A parameter N is calculated as follows:

If blocks U and L are available (i.e. in the same coded slice), N = (Nu  + NL)/2

If only block U is available, N=NU ; if only block L is available, N=NL ; if neither is available, N=0.


Figure 31 Neighbouring blocks NU and NL

N selects the look-up table (Table 34) and in this way the choice of VLC adapts depending on the number of coded coefficients in neighbouring blocks (context adaptive). Num-VLC0 is “biased” towards small numbers of coefficients; low values of TotalCoeffs (0 and 1) are assigned particularly short codes and high values of TotalCoeff particularly long codes. Num-VLC1 is biased towards medium numbers of coefficients (TotalCoeff values around 2-4 are assigned relatively short codes), Num-VLC2 is biased towards higher numbers of coefficients and FLC assigns a fixed 6-bit code to every value of TotalCoeff.


Choice of look-up table for coeff_token



1 Note: coded_block_pattern (described earlier) indicates which 8x8 blocks in the macroblock contain nonzero
coefficients; however, within a coded 8x8 block, there may be 4x4 sub-blocks that do not contain any
coefficients, hence TotalCoeff may be 0 in any 4x4 sub-block. In fact, this value of TotalCoeff occurs most
often and is assigned the shortest VLC. 


2.  Encode the sign of each T1.

For each T1 (trailing +/-1) signalled by coeff_token, a single bit encodes the sign (0=+, 1=-). These are encoded in reverse order, starting with the highest-frequency T1.


3.  Encode the levels of the remaining non-zero coefficients.

The level (sign and magnitude) of each remaining non-zero coefficient in the block is encoded in reverse order, starting with the highest frequency and working back towards the DC coefficient. The choice of VLC table to encode each level adapts depending on the magnitude of each successive coded level (context adaptive). There are 7 VLC tables to choose from, Level_VLC0 to Level_VLC6. Level_VLC0 is biased towards lower magnitudes; Level_VLC1 is biased towards slightly higher magnitudes and so on. The choice of table is adapted in the following way:

(a) Initialise the table to Level_VLC0 (unless there are more than 10 non-zero coefficients and less than 3 trailing ones, in which case start with Level_VLC1).

(b)  ) Encode the highest-frequency non zero coefficient.

(c)  If the magnitude of this coefficient is larger than a pre-defined threshold, move up to the next VLC table.

In this way, the choice of level is matched to the magnitude of the recently-encoded coefficients. The thresholds are listed in Table 35; the first threshold is zero which means that the table is always incremented after the first coefficient level has been encoded.


Thresholds for determining whether to increment level table number


4.  Encode the total number of zeros before the last coefficient.

TotalZeros is the sum of all zeros preceding the highest non-zero coefficient in the reordered array. This is coded with a VLC. The reason for sending a separate VLC t   indicate TotalZeros is that many blocks contain a number of non-zero coefficients at the start of the array and (as will be seen later) this approach means that zero-runs at the start of the array need not be encoded.


5.  Encode each run of zeros.

The number of zeros preceding each non-zero coefficient (run_before) is encoded in reverse order. A run_before parameter is encoded for each non-zero coefficient, starting with the highest frequency, with two exceptions:

(a)  If there are no more zeros left to encode (i.e. ∑[run_before] = TotalZeros), it is not necessary to encode any more run_before values.

(b)  It is not necessary to encode run_before for the final (lowest frequency) non-zero coefficient.

The VLC for each run of zeros is chosen depending on (a) the number of zeros that have not yet been encoded (ZerosLeft) and (b) run_before. For example, if there are only 2 zeros left to encode, run_before can only take 3 values (0,1 or 2) and so the VLC need not be more than 2 bits long; if there are 6 zeros still to encode then run_before can take 7 values (0 to 6) and the VLC table needs to be correspondingly larger.


CAVLC Examples

In all the following examples, we assume that table Num-VLC0 is used to encode coeff_token.

Encoding example


The output array is “built up” from the decoded values as shown below. Values added to the output array at each stage are underlined.

Decoding example



Note 1: Level (3), with a value of -3, is encoded as a special case. If there are less than 3 T1s, then the first non-T1 level will not have a value of +/-1 (otherwise it would have been encoded as a T1). To save bits, this level is incremented if negative (decremented if positive) so that +/-2 maps to +/-1, +/-3 maps to +/-2, and so on. In this way, shorter VLCs are used.

Note 2: After encoding level (3), the level_VLC table is incremented because the magnitude of this level is greater than the first threshold (which is 0). After encoding level (1), with a magnitude of 4, the table number is incremented again because level (1) is greater than the second threshold (which is 3). Note that the final level (-2) uses a different code from the first encoded level (also –2).


Further reading

Iain E Richardson, “The H.264 Advanced Video Compression Standard”, John Wiley & Sons, 2010.

About the author

Vcodex is led by Professor Iain Richardson, an internationally known expert on the MPEG and H.264 video compression standards. Based in Aberdeen, Scotland, he frequently travels to the US and Europe.

Professor Richardson is the author of “The H.264 Advanced Video Compression Standard”, a widely cited work in the research literature. He has written three further books and over 50 journal and conference papers on image and video compression. He regularly advises companies on video codec technology, video coding patents and mergers/acquisitions in the video coding industry. Professor Richardson leads an internationally renowned image and video coding research team, contributes to the MPEG industry standards group and is sought after as an expert witness and litigation consultant.