ISSN: 1693-6930
TELKOMNIKA Vol. 13, No. 4, December 2015 : 1225 – 1232
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Figure 1. Block diagram of SCCC: a SCCC encoder, b SCCC decoder
2.2. Parallel Concatenated Convolutional Codes PCCCs
Figure 2a shows the block diagram of a PCCC encoder. There are two RSC encoders of
rate 12 in parallel, separated by a pseudo-random interleaver. A natural rate for such a code is
13 one systematic bit and two parity bits for one data bit. The multiplexer converts two or more parallel sequences to a single serial sequence.
Figure 2b, shows the decoding process of PCCC. The de-multiplexer block converts the serial data that are received to parallel data. During the first iteration,
λU
1
,I and λU
2
,I are set to zero.
λU
1
,O are passed through interleaver
π
to obtain λU
2
,I, while λU
2
,O is de- interleaved
1
π
to obtain λU
1
,I to start the second iteration. At the final iteration, λU
2
,I and λU
2
,O will be added together, and a hard decision is made on the summation to obtain the estimated information bits.
Figure 2. Block diagram of PCCC: a PCCC encoder, b PCCC decoder
Not used
a
Information bits Encoder 1
rate=12 Encoder 2
rate=12
π
Multiplexer U
1
U
2
To channel
b
Received data SISO Decoder
1 SISO Decoder
2
π
π
-1
De-multiplexer
, 1
C I
, 2
C I
, 1
C O
, 2
C O
, 1
U I
, 2
U I
, 1
U O
, 2
U O
Estimated output Not used
Not used
a
Outer encoder
rate=kl
π
UO Inner
encoder rate=ln
UI CO CI
b
SISO Inner SISO Outer
π
-1
π ,
CI I
, CI O
,
CO O
, UI I
,
UI O
, UO O
Not used
, CO I
,
UO I
From demodulator
TELKOMNIKA ISSN: 1693-6930
Enhancement the Performance of OFDM based on Multiwavelets Using … Sameer A. Dawood
1228
2.3. SISO Decoding Algorithm
The SISO module is a four-port device that accepts two input sequences and gives two output sequences at any time. The two input vectors of SISO at time t are
λ
t
C,I, which is a prior information LLR of a codeword and
λ
t
U,I, which is a prior information LLR of information word. While the two output vectors at time t are
λ
t
C,O, which is the extrinsic information LLR of a codeword and
λ
t
U,O, which is the extrinsic information LLR of information word. SISO Log-MAP decoder uses the max operation which is defined as [15]:
max ln
e
j
a j
j
a
2 The SISO Log-MAP algorithm requires a forward and backward recursion. The forward
recursions of state s at time t t=0, 1,........, 2
m
-1 are given by:
1 :
1 1
max ,
,
E
k n
S j
j j
j t
t t
t e s
e s
j j
s s
e u
e u
I c
e c
I
3 The backward recursions of state s at time t t=2
m
-1, 2
m
-2,........,0 are given by:
1 1
1 :
1 1
max ,
,
E
k n
E j
j j
j t
t t
t e s
e s
j j
s s
e u
e u
I c
e c
I
4 where: e describes the transition edge between states of the trellis at time instants t and t+1,
s
S
e is the starting state of edge e, s
E
e is the ending state of edge e, ue is the input symbol of edge e, ce is the output symbol of edge e, kn is the code rate, and m is the
maximum number of stages memory size in the encoder. The forward and backward recursions will be initialized as [15]:
s s
s otherwise
5 1
2
m
s
6
Then, the two outputs of the SISO decoder at time t are defined as:
1 :
1 1
1 :
1 1
, max
, max
,
j j
n j
S j
j E
t t
t t
e u e
j n
S j
j E
t t
t e u
e j
u O
s e
c e
c I
s e
s e
c e
c I
s e
7
1 :
1 1
1
1 :
1 1
1
, max
, ,
max ,
,
j
j
k n
j S
i i
i i
E t
t t
t t
e c e
i i
i j
k n
S i
i i
i E
t t
t t
e c e
i i
i j
c O s
e u e
u I c e
c I s
e
s e
u e u I
c e c I
s e
8
ISSN: 1693-6930
TELKOMNIKA Vol. 13, No. 4, December 2015 : 1225 – 1232
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3. Proposed System
