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R CORRECTING CODING AND DECODING
e, respectively, equal
' < n of matrix P is
lj
rs equal to zero.
10 O
Pe ,,~
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1263
nce
e of RSC and NSCtrum and their BER.ade up of two sets
ed from two series
unction T(D, N) [6]
(d)Dd (9)
(d)Dd (10) ~
e, a(d) is
the numberthe "null" path and
input sequences {dk}
from the "null" path.
the transfer function
first coefficients a(d)
e trellis by using ancients W(d), a tight
e calculated for large
).
(11)
ith binary modulation
to
lEb(1 2
)IVoJ
ion bit to noise powerrate
.
ave been investigated
o that of NSC codes,
ER. Coefficients a(d)
s but the coefficients
ency to increase morecients {VV~Nsc(d)} of
whatever the memory- nar --J- : ^T**'^*'~
lO -I
10 -2
lO -3
lO -4
lO -5
10 -6
O 1 2 3 4 5 6 7 8
Eb/No (dB)
Fig. 3.
P* of punctured RSC and NSC codes for different values of rate Rand memory v = 6
,generators Gl = 133,G2 = 1 71.
is
approximately 0.8 dBit
reaches 1.75 dB.
atR = 2/3, whereas at R = 314,
HI. PARALLEL CONCATENATION WITH NoNUNIFORM INTERLEAVING: TURBO-CODE
A. Construction of the Code
The use of systematic codes enables the construction of
a concatenated encoder in the form given in Fig. 4,
called
parallel concatenation. The data flow (dk at time h)
goesdirectly to a first elementary RSC encoder Cl and after
interleaving, it
feeds (d~ at time k)
a second elementary
RSC encoder C2.
These two encoders are not necessalily
identical. Data dk is
systematically transmitted as symbol
Xk and redundancies Ylk and Y2k Produced by Cl and C2
may be completely transmitted for an R = I /3
encoding or
I
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,
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.
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(~;~:/;~~')
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h* h,
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警二
Eb／No（dB）
4
theOretiCaI
1imit
4
5 －
0
1
iterative decoding (p
:::1,""'18) of a rate R :=
1/9-
4,
generators Gl =: 37,
G'2 =: 21, with interleaving卵：
Fig. 9.
BER given
encoder, Inemory v256 x 256.
B. Interleaving
The interleaver ismade up of anM ･
I~AI matrix and bits {dk}
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