King Fahd University of Petroleum and Minerals
Electrical Engineering Department
Mr. Ali Hussain Mugaibel
Dr. Maan Kousa
16 March 1999
CETEM’ 99
Topics of Discussion

Turbo Codes
Introducing turbo codes.
 Turbo Encoders
 Turbo Decoders





Promises
Challenges
Can we Improve TC ?
Conclusion
Mugaibel/Kousa Turbo Codes: Promises and Challenges , CETEM' 99
Coding
Source
Channel
Convolutional
Block
X0
+
Input
1011 101101
101101
010110
0010110
1001011
01D
10D
10D
0
D
+
(a)
Mugaibel/Kousa Turbo Codes: Promises and Challenges , CETEM' 99
X1
What are turbo codes ?

New class of CC.
Introduced in 1993 by Berrou, Glavieux and
Thitimajashima.


Perform close to Shannon limit in terms of BER.
Use iterative scheme with reference to the turbo
engine principle.

Mugaibel/Kousa Turbo Codes: Promises and Challenges , CETEM' 99
Turbo Encoder

More than one CC are linked in parallel
by interleavers.
Information
Source
PAD
X0
Interleaver
Enc 1
X1
Enc 2
X2
Puncturing &
Parallel/Serial
MUX
Figure 1: Simplified Turbo Encoder
Mugaibel/Kousa Turbo Codes: Promises and Challenges , CETEM' 99
to the
channel
Turbo Encoder
Important factors :

RSC encoders
 Termination
 Puncturing

Input
X0
+
Input
D
D
D
D
X0
+
+
(a)
X1
D
D
D
+
(b)
Figure 2: (a) Classical Non-Recursive Non- Systematic Code
(b) Recursive Systematic Code
Mugaibel/Kousa Turbo Codes: Promises and Challenges , CETEM' 99
D
X1
Turbo Decoder

SOVA: SOVA is supposed to be the least computation
intensive method compared with MAP, LogMAP,...
(Interleaver 1)-1
Decoder 1
r0
r1
Interleaver 1
Decoder 2
DEMUX
Mugaibel/Kousa Turbo Codes: Promises and Challenges , CETEM' 99
Turbo Decoder

Important factors :
Iteration
 DEMUX
 Synchronization


Main idea

The decoder will pass the hard decision
together with a reliability estimate of this
decision to the next decoder
 p( x  1 y ) 
 p(uk  1) 
k ,1
k ,1
  ln 
L(uk ) I  ln 

p(uk  1) 
 p( xk ,1  1 yk ,1 ) 



Mugaibel/Kousa Turbo Codes: Promises and Challenges , CETEM' 99
Promises



The major promise of turbo codes is their
astonishing performance of bit error rate (BER) at
relatively low Eb/N0.
For AWGN channel: for a frame size of
256256=65536 bits we can achieve a BER=10-5
at only Eb/N0=0.7dB, which is very close to
Shannon limit.
For a Rayleigh fading channel: a BER=10-5 can
be achieved at Eb/N0=4.3dB which represents a
gain of 2.3dB as compared to classical
convolutional codes with similar complexity.
Mugaibel/Kousa Turbo Codes: Promises and Challenges , CETEM' 99
Challenges





Delay: associated with interleaver and the
iterative decoding algorithm.
Complexity: in the optimal decoding algorithm.
Can we use Turbo Codes for real time
applications ?
Can we improve Turbo Codes ?
Can we introduce a mathematical model for the
evaluation of different Turbo Codes ?
Mugaibel/Kousa Turbo Codes: Promises and Challenges , CETEM' 99
Can We improve Turbo Codes ?
A good understanding of the code ingredients will help to
improve the code.

If we understand what the interleaver is doing we can
introduce short frames suitable for real time applications.

Puncturing is very important to increase the rate to an
applicable value.

The decoding algorithm can be sufficiently simplified yet
with very minor degradation.

Mugaibel/Kousa Turbo Codes: Promises and Challenges , CETEM' 99
Conclusion
We have reviewed Turbo Codes and some of their promises
and challenges.


Turbo Codes are attracting more and more applications.
More work can be done in understanding the effects of the
codes ingredients on the performance.


The decoding delay is a major challenge in turbo coding
Turbo Coding can be applied as a case study for many of the
existing systems ( GSM, IS….)

Mugaibel/Kousa Turbo Codes: Promises and Challenges , CETEM' 99