**ISO/IEC 10918-1 : 1993(E)**

**F.1.4.4**

**Statistical models**

An adaptive binary arithmetic coder requires a statistical model. The statistical model defines the contexts which are used

to select the conditional probability estimates used in the encoding and decoding procedures.

Each decision in the binary decision trees is associated with one or more contexts. These contexts identify the sense of the

MPS and the index in Table D.3 of the conditional probability estimate Qe which is used to encode and decode the binary

decision.

The arithmetic coder is adaptive, which means that the probability estimates for each context are developed and

maintained by the arithmetic coding system on the basis of prior coding decisions for that context.

**F.1.4.4.1**

**Statistical model for coding DC prediction differences**

The statistical model for coding the DC difference conditions some of the probability estimates for the binary decisions on

previous DC coding decisions.

**F.1.4.4.1.1**

**Statistical conditioning on sign**

In coding the DC coefficients, four separate statistics bins (probability estimates) are used in coding the zero/not-zero (V

=

0) decision, the sign decision and the first magnitude category decision. Two of these bins are used to code the V

=

0

decision and the sign decision. The other two bins are used in coding the first magnitude decision, Sz < 1; one of these

bins is used when the sign is positive, and the other is used when the sign is negative. Thus, the first magnitude decision

probability estimate is conditioned on the sign of V.

**F.1.4.4.1.2**

**Statistical conditioning on DC difference in previous block**

The probability estimates for these first three decisions are also conditioned on Da, the difference value coded for the

previous DCT block of the same component. The differences are classified into five groups: zero, small positive, small

negative, large positive and large negative. The relationship between the default classification and the quantization scale is

shown in Figure F.10.

5

4

3

2

1

0

+1

+2

+3

+4

+5

0

TISO1420-93/d080

. . .

. . .

large

small

+ small

+ large

DC difference

Classification

**Figure F.10 Conditioning classification of difference values**

Figure F.10 [D80] = 3 cm = 117 %

The bounds for the "small" difference category determine the classification. Defining L and U as integers in the range 0 to

15 inclusive, the lower bound (exclusive) for difference magnitudes classified as "small" is zero for L

=

0, and is 2

L1

for

L > 0.

The upper bound (inclusive) for difference magnitudes classified as "small" is 2

U

.

L shall be less than or equal to U.

These bounds for the conditioning category provide a segmentation which is identical to that listed in Table F.3.

**F.1.4.4.1.3**

**Assignment of statistical bins to the DC binary decision tree**

As shown in Table F.4, each statistics area for DC coding consists of a set of 49 statistics bins. In the following

explanation, it is assumed that the bins are contiguous. The first 20 bins consist of five sets of four bins selected by a

context-index S0. The value of S0 is given by DC_Context(Da), which provides a value of 0, 4, 8, 12 or 16, depending on

the difference classification of Da (see F.1.4.4.1.2). The remaining 29 bins, X1,...,X15,M2,...,M15, are used to code

magnitude category decisions and magnitude bits.

**100**

**CCITT Rec. T.81 (1992 E)**