process. Furthermore, it is also possible to employ more than two component codes. However, in this paper it concentrates entirely on the standard turbo encoder structure using two RSC codes.
International Journal of Scientific & Engineering Research Volume 2, Issue 7, July-2011 1
ISSN 2229-5518
Performance Study of Turbo Code with
Interleaver Design
Mojaiana Synthia, Md. Shipon Ali
Abstract— This paper begins with an investigation of the optimization of binary turbo code through good interleaver design. For this purpose, different types of interleaver have designed here and have evaluated their performance. Basically the performances of the turbo code using block interleaver, helical interleaver, random interleaver and odd-even interleaver have evaluated. From this investigation it has been seen that for small code length the performance of the block interleaver is superior in non-puncturing case and the performance of the odd-even interleaver is superior in puncturing case, but for large code length the performance of the random interleaver is better in both of puncturing and non-puncturing condition. In this paper, it has investigated that the performance of the odd-even interleaver (block interleaver with odd number of rows and columns) significantly increased in puncturing conditions.
Index terms— Turbo encoder; Turbo decoder; Interleaver; code rate; Puncturing; Nonpucturing.
—————————— • ——————————
ue to increasing demand for information exchange in modern civilization, the transfer of information
from the source to its destination has to be done in such a way that the quality of the received information should be as close as possible to the quality of the transmitted information. Channel codes are used as an invaluable tool for this purpose. The channel encoder adds code
process. Furthermore, it is also possible to employ more than two component codes. However, in this paper it concentrates entirely on the standard turbo encoder structure using two RSC codes.
Input Bits
RSC Encoder 1
Output Bits
bits to the transmission bit stream, based on the data bits
at its input. These extra bits a reused by the channel decoder at the receiver to correct errors introduced into the transmission stream by a noisy or fading channel. But, there are two main disadvantages of error
Interleaver
Puncturing
RSC Encoder 2
correcting codes. Firstly, the injection of extra bits into
the transmission stream, thus increasing the bandwidth needed to transmit the signal. A second disadvantage is that they add complexity to the design of a communications system. In this paper some technique has introduced to overcome these problems.
A general Turbo encoder is shown in Figure 2.1. It employs two identical systematic recursive Convolutional encoders connected in parallel with an interleaver preceding the second recursive convolutional encoder. The two recursive convolutional encoders are called the constituent encoders of the Turbo encoder. The information bits are encoded by both RSC encoders. The data frame, length of size N, inserts directly into the first encoder and after interleaving of length N, it feeds the second encoder. Therefore, N systematic bits can generate 2N parity bits and its gives a code rate of 1/3. However, it can be removed some of the parity bits in order to increase the coding rate by means of puncturing
Fig (2.1): General Turbo Encoder.
The interleaver design is a key factor which determines the good performance of a turbo code. The output sequences of RSC encoder usually have high weight. However, some input sequences still cause the output sequence of RSC encoder to generate low weight codeword. Therefore, the interleaver scrambles the input sequence and generates randomness to the input sequence as a result high codeword can obtain. Some of the useful inter-leaver used in turbo code is discussed in the following sections.
Block interleaver is easy to implement in practice. This simplest interleaver is a memory in which data is written row–wise and read column–wise. It is also known as the “row–column” interleaver.
IJSER © 2011 http://www.ijser.org
International Journal of Scientific & Engineering Research Volume 2, Issue 7, July-2011 2
ISSN 2229-5518
Table (3.A.1): Writing data row–wise in memory. Table (3.A.2): Reading data column–wise from memory.
A helical interleaver writes data into row–wise but reads data diagonal–wise. An example of helical interleaver is shown below:
independent RSC encoders, except the systematic information only need be transmitted for one of the encoders. The decoder can reconstruct the systematic bits for the other encoders because it knows the interleaving patterns that were used. Thus, the decoder can be decomposed into T convolutional decoders with each one operating on the output of a single constituent encoder. In order to get the best possible estimate of the original message, these separate decoders must be able to share the results of their calculations. To accomplish this, turbo decoders use iterative feedback decoding. Figure 4.1 shows a schematic of a turbo decoder for the classical turbo code with T=2.
DE-INT
Table (3.B.1): Writing data row–wise in memory. D E
×
Table (3.B.2): Reading data diagonal–wise from memory.
U
X
An odd-even interleaver is a block interleaver in which
the number of rows and columns must be odd numbers.
The most used turbo code interleaver is the random
D E C
1
. . . . . . . . . .
I N T
INT
D E C
2
DE-INT
interleaver. It basically generates a mapping between the input and the output positions. It can be designed for arbitrary length of input bits. If the length of the input is N, the mapping set will have N! combinations and chooses one combination to permute the input bits. A simple random interleaver to permute data is shown below:
X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 | X9 |
Random Interleaver
X8 | X4 | X3 | X9 | X2 | X6 | X7 | X1 | X5 |
Fig (3.D.1): The random interleaver with length 10.
Fig (4.1): General Turbo Decoder.
This turbo decoder corresponds to the turbo encoder of figure 2.1. The first decoder uses the systematic
information xk , the output from the first constituent encoder y1k , and a priori information from the second decoder La2,k , to calculate soft estimates of the original
data in the block known as a log-likelihood ratio (LLRs),
il1. The systematic and a priori information are subtracted from il1 in order to prevent positive feedback.
What is left over is the new information calculated by
the first decoder Le1,k , known as the extrinsic
information. This extrinsic information will be used as a
priori information by the second decoder. The second
decoder uses this a priori information along with the
systematic information, and the output of the second
constituent encoder y2k . However, y2k was calculated from an interleaved version of xk , so both the systematic
information and extrinsic information from the first
decoder must be interleaved (forming xk
and La1,k ,
In a turbo encoder with T constituent encoders, the
encoder output contains a single systematic output and
T parity outputs from the RSC encoders (assuming no
puncturing), T – 1 of which operate on an interleaved
version of original data block. Thus, the output of the
turbo encoder can be viewed as the output of T
respectively) before being used in the second decoder. The second decoder produces the extrinsic information
Le2,k that is de-interleaved and then fed back to the first encoder to be used as a priori information La2,k . After the
first decoding cycle has completed, the decoder is not
taking in new inputs. Instead, it is iterating toward a
IJSER © 2011 http://www.ijser.org
International Journal of Scientific & Engineering Research Volume 2, Issue 7, July-2011 3
ISSN 2229-5518
best estimate of the transmitted data using the received values that it now has stored in memory. After I iterations, the feedback loop is broken and the LLRs
K = 3, G0 = 7, G1 = 5; R = 1/3; Log-MAP Algorithm; iterations = 8; 4,000 Blocks
0
10
Random (60*60)
block (60*60) Helical (60*60)
produced by the second decoder are de-interleaved one -1
final time to put them in the same order as the original
data block and a hard limiter makes the final bit
decisions to produce the decoded block.
In this paper, interleavers effects have investigated into two different conditions depend on transmission data rate. One is non-puncturing condition where all of parity bits are transmitted along systematic bits. And other is puncturing condition where some of parity bits are transmitted along systematic bits.
Figure 5.A.1, 5.A.2 and 5.A.3 shows the BER performance of the turbo code using random interleaver, helical interleaver and block interleaver; within non- puncturing situations. From figure 5.A.1, it is observed that the performance of both of the block interleaver and helical interleaver are better than the random interleaver for small code length input data. Again, it is also shown that for large code length input data the performance of random interleaver is better than others as figure 5.A.3. The performance of block interleaver and helical interleaver are almost same for any code length of input data.
K = 3, G0 = 7, G1 = 5; R = 1/3; Log-MAP Algorithm; 4,000 Blocks
0
-3
10
-4
10
-5
10
0 0.5 1 1.5 2 2.5
Signal-to-noise ratio, Eb/No (dB)
Fig (5.B.2): BER performance with different interleavers.
K = 3, G0 = 7, G1 = 5; R = 1/3; Log-MAP Algorithm; Iteration = 8; 4,000 Blocks
0
10
Random (70*70)
Block (70*70) Helical (70*70)
-1
10
-2
10
-3
10
-4
10
-5
10
0 0.5 1 1.5 2 2.5
10
Random (40*40)
Block (40*40) Helical (40*40)
Signal-to-noise ratio, Eb/No (dB)
Fig (5.A.3): BER performance with different interleavers.
K = 3, G0 = 7, G1 = 5; R = 1/2; Log-MAP Algorithm; Iteration = 8; 4,000 Blocks
0
10
-1 Random (40*40)
10 block (40*40) Helical (40*40)
-1
10
-2
10
-2
10
-3
10
0 0.5 1 1.5 2 2.5
Signal-to-noise ratio, Eb/No (dB)
Fig (5.A.1): BER performance with different interleavers.
Bit puncturing is required in order to assure the efficient use of available bandwidth. Turbo code performance using random interleaver, helical interleaver and block interleaver within puncturing situations are shown in figure 5.B.1, 5.B.2 and 5.B.3.
-3
10
0 0.5 1 1.5 2 2.5
Signal-to-noise ratio, Eb/No (dB)
Fig (5.B.1): BER performance with different interleavers.
IJSER © 2011 http://www.ijser.org
International Journal of Scientific & Engineering Research Volume 2, Issue 7, July-2011 4
ISSN 2229-5518
K = 3, G0 = 7, G1 = 5; R = 1/2; Log-MAP Algorithm; Interations = 8; 4,000 Blocks
0
10
Random (60*60)
block (60*60) Helical (60*60)
K = 3, G0 = 7, G1 = 5; R = 1/2; Log-MAP Algorithm; Iteration = 8; 5,000 Blocks
0
10
Random (41*41)
Odd-even (41*41) Helical (41*41)
-1
10
-1
10
-2
10
-3
10 -2
10
-4
10
-5
10
0 0.5 1 1.5 2 2.5
Signal-to-noise ratio, Eb/No (dB)
-3
10
0 0.5 1 1.5 2 2.5
Signal-to-noise ratio, Eb/No (dB)
Fig (5.B.2): BER performance with different interleavers.
Fig (5.B.4): BER performance with different interleavers.
K = 3, G0 = 7, G1 = 5; R = 1/2; Log-MAP Algorithm; Iteration = 8; 4,000 Blocks
0
K = 3, G0 = 7, G1 = 5; R = 1/2; Log-MAP Algorithm; Iteration = 8; 4,000 Blocks 10
0
10
Random (70*70)
block (70*70)
Random (61*61) Odd-even (61*61) Helical (61*61)
-1 Helical (70*70)
10
-1
10
-2
10
-3
10 10
-4
10
-5
10
0 0.5 1 1.5 2 2.5
-3
10
0 0.5 1 1.5 2 2.5
Signal-to-noise ratio, Eb/No (dB)
Signal-to-noise ratio, Eb/No (dB)
Fig (5.B.3): BER performance with different interleavers.
Fig (5.B.5): BER performance with different interleavers.
K = 3, G0 = 7, G1 = 5; R = 1/2; Log-MAP Algorithm; Iteration = 8; 5,000 Blocks
0
From these figures it is observed that the resultant 10
performances are almost same as that obtained in non-
puncturing conditions except that the performance of -1
10
helical interleaver is better than the block interleaver.
In puncturing case, the performance of block -2 interleaver significantly increased when its number of 10 rows and columns are odd (odd-even interleaver). The performances of turbo code using odd-even interleaver -3 comparison with the helical and random interleaver are
shown in figure 5.B.4, 5.B.5 and 5.B.6. Also, it is observed
that the performance of odd-even interleaver is better 10
than the helical interleaver for any code length of input
data. Again, for below of (60×60) code length the odd-
Random (71*71) Odd-even (71*71) Helical (71*71)
even interleaver’s performances are better than random interleaver. Also for large code length of input data the performance of the random interleaver is still better than others.
10
0 0.5 1 1.5 2 2.5
Signal-to-noise ratio, Eb/No (dB)
Fig (5.B.6): BER performance with different interleavers.
IJSER © 2011 http://www.ijser.org
International Journal of Scientific & Engineering Research Volume 2, Issue 7, July-2011 5
ISSN 2229-5518
In this paper, effects of interleavers have studied in details with both of the puncturing and non-puncturing case. From there it has seen that for non-puncturing case, the performance of the block interleaver and helical interleaver are almost same and better than the random interleaver at small code length data transmission. But, for large code length data transmission the random interleaver perform much better than both of the block interleaver and helical interleaver. In puncturing case, the performances of these interleaver’s are almost same as that obtained in non-puncturing conditions except that the performance of helical interleaver is better than the block interleaver. But in puncturing case, that the performances of odd-even interleaver is better than the helical interleaver. This improvement is occurred because it can only possible to transmit at least one parity bit for each systematic bit by using odd-even interleaver. However, for below of (60×60) code length the odd-even interleaver’s performances are better than the performance of random interleaver.
[1] Robert H. Morelos-Zaragoza, “The Art of Error Correcting
Coding,” SONY Computer Science Laboratories Inc, Japan, 2002.
[2] Jason R. Hess, “Implementation of a Turbo Decoder on a
Configurable Computing Platform,” Virginia Polytechnic Institute and State University, USA, 1999.
[3] Alain Glavieux, “Channel Coding in Communication networks
From Theory to Turbo codes,” ISTE Ltd, USA, 2007.
[4] T. E. Hunter,” Coded Cooperation: A New Framework for User
Cooperation in Wireless Networks,” Ph.D. dissertation, The
University of Texas at Dallas, May, 2004.
[5] C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon Limit Error- correcting Coding and Decoding: Turbo-Codes,” the International Conference on Communications, (Geneva, Switzerland), pp.1064 in1070, May, 1993.
[6] S. Le Go, A. Glavieux, and C. Berrou, “Turbo-Codes and High
Spectral Efficiency Modulation,” Proceedings of IEEE international conference on communications, New Orleans, LA. pp. 645-649, May 1-5, 1994.
[7] Joachim Hagenauer, “Iterative Decoding of Binary Block and
Convolutional Codes,” IEEE Transactions on Information Theory, Vol. 42, No. 2, March 1996.
[8] Mark Bingeman, “Symbol-Based Turbo Codes for Wireless
Communications,” Electrical and Computer Engineering
Discipline, Waterloo, Ontario, Canada, 2002.
[9] K. V. Ravi and Tam Soh Khum, “Performance of Turbo TCM in Wideband CDMA Applications,” Department of Electrical Engineering, National University of Singapore, 2000.
[10] D. Gnaedig, E. Boutillon and M. Jezequel “Design of Three-
Dimensional Multiple Slice Turbo Codes,” EURASIP Journal on
Applied Signal Processing, 2005.
[11] Fu-hua Huang, “Iterative Turbo Code. Decoder” John Wiley &
Sons, New York, 2000.
[12] Bernard Sklar, “Digital Communications: Fundamentals and
Applications,” Second Edition, 2001.
[13] Matthew C. Valenti and Jian Sun, “Handbook of RF and
Wireless Technologies,” John Wiley & Sons, New York, 2003.
[14] Salma Ben Jamaa, Michel Kieffer and Pierre Duhamel, “Exact MAP Decoding of Cabac Encoded Data,” University of Paris, France.
[15] George White “Optimised Turbo Codes for Wireless
Channels,” Ph.D. Thesis, Department of Electronics, University of
York, UK, October, 2001.
[16] Jinghu Chen, Marc P. C. Fossorier and Shu Lin, “Bi-directional
SOVA Decoding for Turbo-codes,” Department of Electrical
Engineering, University of Hawaii, USA.
• Author1: Mojaiana Synthia, Electronics & Communication Engineering Discipline, Khulna University, Bangladesh.
• Author2: Md. Shipon Ali, Grameenphone Limited, Dhaka, Bangladesh
IJSER © 2011 http://www.ijser.org