Digital Signal Processing Reference
In-Depth Information
The probability of symbol
a
is
p
=
0.8
, the source correlation coefficient is
. The encoding process can be expressed as follows.
Step1: Initialize the coding interval to {0, 8, 0,
ρ
=
0.3
Uf
=
8,
=
1
m
Null
.
Step2: Partition the current coding interval
Ic
according to source probability and
correlation coefficient,
}
a
a
a
b
b
b
I
=
[, ]
l
u
,and
I
=
[
l
,
u
]
.
c
c
a
c
b
c
Step3: Normalize
I
and
I
as need as necessary.
bb
lu fs
are obtained. If they have been never
appeared before, add them as new states, otherwise go to step 5.
Step5: Repeat step 2,3 and 4 until there is no new state to appear.
In order to obtain the expected distributed rate, puncturing is used in DQAC. The
puncturing segment is decided by theoretical rate
Rq
, expected rate
Rt
, the length of
source sequence
Lx
and the length of encoded codeword
Ls
. Since there are
(
aa
lu fs
and {
Step4: Two states {
,
,
, }
,
,
, }
RqRt Ls
−×
)
bits to be punctured, so the factual puncturing segment is
(
Rq
−×
Rt
)
Ls
/
Lx
−
1
bits. However, if (
RqRt Ls Lx
−×>
)
/ 2
, the above segment
should be bit position not to be punctured.
The decoding of DQAC can use improved Viterbi algorithm or BCJR algorithm,
along with side information and the knowledge of source correlation.
2.4
Proposed Distributed Arithmetic Coding
The encoding of DOAC is easier than that of DQAC, especially the expected coding
rate can be obtained conveniently by adjusting a parameter without changing the
encoding strategy, let alone puncturing. However, using M-algorithm to decode
DOAC needs more memories and more computational complexity to get better
decoding performance. To the contrary, decoding DQAC becomes easier because of
the FSM representation. For the above reasons, a new DAC scheme is proposed.
The proposed DAC implements the encoding process using overlapped interval as
that in DOAC to produce wanted coding rate, but during encoding process record the
FSM representation as DQAC. Thus, the proposed DAC does not need puncturing to
get the expected coding rate, and can softly and jointly decode with lower complexity
to obtain better performance. Here, List-Viterbi algorithm [8].
3
Simulation Results
The DAC schemes described above are applied in the following experiment,
assuming that the side information
Y
is available at the decoder. Two situations are
considered in the experiment, the source length and probability, to observe and study
how they affect the performance of DAC. Two different length binary uncorrelated
source sequences with symmetric probability
pp
0
==0.5
and asymmetric probability
p
=0.9 and
p
=0.1
are encoded respectively. The same source sequence is encoded
0
1
