Page 46 - Video Coding for Mobile Communications Efficiency, Complexity, and Resilience

Section 2.5. Video Coding Basics 23

the quantization process can be implemented at the encoder using

s
sˆ= NINT ; (2.8)

s
where NINT[·] is the operation of rounding to the nearest integer and ˆ is
called the quantization index. It is the quantization index that is encoded and
sent to the decoder. The decoder can then dequantize this index to obtain the
reconstructed output as follows:
s˙= · ˆs: (2.9)

This type of quantizer is also known as a threshold quantizer, because it
quantizes to zero all those inputs whose magnitudes are below a threshold.
As will be discussed later, this type of quantizer is usually used in transform
coding to reduce the number of transform coeGcients that need to be encoded.
Another example of uniform threshold quantizers is illustrated in Figure 2.5(b).
In this case, the quantization interval around zero has been extended to form
a dead zone. This causes more nonsigni cant inputs to be quantized to zero
and, thus, increases compression. The quantization equation for this quantizer
is given by

s
sˆ= FIX ; (2.10)

where FIX[·] is the operation of rounding to the nearest integer toward zero
(i.e., truncation). The corresponding dequantization equation is given by

s
s
˙ s = · ˆ + SIGN(ˆ) · ; (2.11)
2

 +1;a¿0;


SIGN(a)= 0;a =0; (2.12)
 −1;a¡0:


Scalar quantizers can also be nonuniform. In this case, more reconstruction
levels are assigned to more signi cant subintervals within the input range. This
yields a higher overall accuracy.
2.5.5 Symbol Encoding
Another key element of video coding systems is the symbol encoder. This
assigns a codeword to each symbol at the output of the quantizer. The symbol
encoder must be designed to reduce the coding redundancy present in the set
of symbols. Following are a number of commonly used techniques that can
be applied individually or in combinations.