Signal Processing - September 2016 - 168

partition size. If the partition size is 16 #
16, then a 16 # 16 transform is applied;
else if the partition size is 8 # 8, an 8 # 8
transform is applied; otherwise, a 4 # 4
transform is applied. The inverse transform processes are specified as

Table 3. Interpolation filter coefficients
for chroma components.
Position

Filter Coefficients

1/8

{−4, 62, 6, 0}/64

2/8

{-6, 56, 15, −1}/64

3/8

{−5, 47, 25, −3}/64

4/8

{−4, 36, 36, −4}/64

5/8

{−3, 25, 47, −5}/64

6/8

{−1, 15, 56, −6}/64

7/8

{0, 6, 62, −4}/64

R N # N = (T T N # N ) C N # N ) T N # N
+ (1 << left_shift)) >> right_shift,
(6)

adaptively determined whether nonreference P-frame coding is used (e.g.,
P0, P1, P2, and P3) or not (e.g., P4,
P5, P6, and P7) for every four frames
based on the temporal correlation that
is measured by the amount of motion
and bitrate in an adaptive manner.

where R N # N is the N # N residual
matrix, TN # N is the N # N transform
matrix, and C N # N is the transformed
N # N matrix. For the 16 # 16, 8 # 8 and
4 # 4 inverse transforms, the parameters
of {N, left_shift, right_shift} are set as
{16, 14, 15}, {8, 4, 5}, and {4, 16, 17}
respectively.

Adaptive block size transform

Logarithmic domain
arithmetic coding

Adaptive block size transforms are
applied on the prediction residuals to
reduce the spatial redundancy. The
transform block size can be either 16 #
16, 8 # 8, or 4 # 4. Integer transforms
of 16 # 16, 8 # 8, and 4 # 4 are derived
by scaling and rounding the DCT cores
of 16 # 16, 8 # 8, and 4 # 4 respectively
[8], [9]. For the intermacroblock partition, if the partition size is 16 # 16, a
16 # 16 transform is applied; otherwise,
an 8 # 8 transform is applied on each 8 #
8 block within this macroblock partition. For the intramacroblock partition,
the transform size is coupled with the

Coding a data symbol involves the following steps: 1) binarization, 2) context
model selection, and 3) arithmetic encoding. For a given nonbinary valued syntax
element, it is uniquely mapped to a binary sequence, a so-called bin string. Each
of the given binary decisions, which are
referred to as a bin in the sequence, enters the context modeling stage where a
context model is selected. Then, the bin
value, along with its associated context
model, is passed to the regular coding
engine or bypass coding where the final
stage of arithmetic encoding together
with a subsequent context updating takes

place. Binary arithmetic coding is based
on the principle of recursive interval
subdivision that involves the following
elementary multiplication operation.
Suppose that an estimate of the probability PMPS (0.5, 1) of the most probable
symbol (MPS) is given, and the given interval is represented by its lower bound,
L, and its width (range), R. Based on
these settings, the given interval is subdivided into two subintervals: one interval
of width, R MPS and R LPS .
R MPS = R) PMPS

(7)

R LPS = R - R MPS .

(8)

An arithmetic coding method in a
the logarithmic domain is adopted as the
entropy coding engine [14]. In the binary arithmetic coder, the multiplication in
the R MPS calculation is substituted with
addition in the logarithm domain. When
an MPS happens, the renewal of range
is given as
LogR MPS = LogR + LogPMPS.

(9)

Assume the value of logR is represented by its integer part s1 and fractional part t1, and the value of Log(RMPS) is
represented by its integer part s2 and
fractional part t2, respectively. When
an LPS happens, the range is updated
as follows:
R LPS = R - R MPS
= 2 -s1 + t1 - 2 -s2 + t2 . 2 -s1 )(1 + t1)
- 2 -s2 ) (1 + t2), since
2 x . 1 + x (0 1 x 1 1) .

(10)

So, R MPS and R LPS are all calculated
by just addtions and shifts operations.

Third
Level

First
Level
P

P

t-12

t-8

P

P

P

P

t-4

P

P

P

P

P

t-2

t-1

t

t+1

P0

IEEE Signal Processing Magazine

Third
Level

p3
p1

First
Level

p2

P4 P5 P6 P7

Figure 8. An adaptive nonreference P coding

Figure 7. The relationship between the current frame with its reference frames.
168

Second
Level

structure.

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September 2016

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Table of Contents for the Digital Edition of Signal Processing - September 2016
