Databases Reference
In-Depth Information
The idea that encoding sequences of outputs can provide an advantage over the encoding
of individual samples was first put forward by Shannon, and the basic results in information
theory were all proved by taking longer and longer sequences of inputs. This indicates that
a quantization strategy that works with sequences or blocks of output would provide some
improvement in performance over scalar quantization. In other words, we wish to generate a
representative set of sequences. Given a source output sequence, we would represent it with
one of the elements of the representative set.
In vector quantization we group the source output into blocks or vectors. For example,
we can treat
L
consecutive samples of speech as the components of an
L
-dimensional vector.
Or, we can take a block of
L
pixels from an image and treat each pixel value as a component
of a vector of size or dimension
L
. This vector of source outputs forms the input to the
vector quantizer. At both the encoder and decoder of the vector quantizer, we have a set of
L
-
dimensional vectors called the
codebook
of the vector quantizer. The vectors in this codebook,
known as
code-vectors
, are selected to be representative of the vectors we generate from the
source output. Each code-vector is assigned a binary index. At the encoder, the input vector
is compared to each code-vector in order to find the code-vector closest to the input vector.
The elements of this code-vector are the quantized values of the source output. In order to
inform the decoder about which code-vector was found to be the closest to the input vector, we
transmit or store the binary index of the code-vector. Because the decoder has exactly the same
codebook, it can retrieve the code-vector given its binary index. A pictorial representation of
this process is shown in Figure
10.1
.
Although the encoder may have to perform a considerable amount of computations in order
to find the closest reproduction vector to the vector of source outputs, the decoding consists of a
table lookup. Thismakes vector quantization a very attractive encoding scheme for applications
in which the resources available for decoding are considerably less than the resources available
for encoding. For example, in multimedia applications, considerable computational resources
Source
output
Reconstruction
Encoder
Decoder
Group
into
vectors
Find
closest
code-vector
Table
lookup
. . .
Unblock
Codebook
Index
Index
Codebook
F I GU R E 10 . 1
The vector quantization procedure.
