International Journal of Scientific & Engineering Research, Volume 3, Issue 7 July-2012 1

ISSN 2229-5518

Improving BER using turbo codes in OFDM


Inderjeet Kaur, Dr. Y.K.Mathur

AbstractOrthogonal Frequency Division Multiplexing (OFDM) has been successfully applied to a wide variety of digital communication applications over the past several years. OFDM is a suitable candidate for high data rate transmission with forward error correction (FEC) methods over wireless channels. OFDM is a suitable candidate for high data rate transmission with forward error correction (F EC) methods over wireless channels.In this paper, the system throughput of a working OFDM system has been enhanced by adding turbo coding. The use of turbo coding and power allocation in OFDM is useful to the desired performance at higher data rates. Simulation is don e over additive white Gaussian noise (AW GN) and impulsive noise (which is produced in broadband transmission) channels.

Index TermsTurbo codes, bit error rate, OFDM, AW GN, Bit Error rate, orthogonal frequency division multiplexing, Signal to Noise Ratio


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With the rapid growth of digital communication in recent years, the need for high speed data transmission is increased. Moreover, future wireless systems are expected to support a wide range of services which includes video, data and voice. One way to transmit this data rate information is to employ well-known conventional single carrier systems. However, since the transmission bandwidth is much larger than the cohe- rence bandwidth of the channel, highly complex equalizers are needed at the receiver for accurately recovering the transmitted information. It has been noticed, that the multi-carrier tech- niques can solve this problem significantly if designed properly. Optimal and efficient design leads to the adaptive implementa- tion of multicarrier systems. During the last decade, OFDM has been the core technology in the physical layer of many wireless communication standards, including WLAN standards such as IEEE802.11g and HIPERLAN/2, as well as digital broadcasting systems such as Terrestrial Digital Video Broadcasting (DVB-T) [1]. Orthogonal frequency division multiplexing (OFDM) is a promising candidate for achieving high data rate transmission in mobile environment. OFDM transmission system offers pos- sibilities for alleviating many of the problems encountered with single carrier systems [2]. OFDM is symbol based, and can be thought of as a large number of low bit rate carriers transmit- ting in parallel. All these carriers transmitted using synchro- nized time and frequency, forming a single block of spectrum. This is to ensure that the orthogonal nature of the structure is maintained [3, 4]. Since these multiple carriers form a single OFDM transmission, they are commonly referred to as ‗subcar- riers‘, with the term of ‗carrier‘ reserved for describing the RF


Inderjeet Kaur is currently pursuing PhD degree program in Computer

Science & Engineering in SinghaniaUniversity, Rajsthan, India, PH-

9711317003. E-mail:
Dr.Y K Mathur is professor and Dean in PDM college of Engineering, Bahadurgarh, India, PH-9711317003. E-mail:
carrier mixing the signal from base band. It has the advantage of spreading out a frequency selective fade over many symbols.
This effectively randomizes burst errors caused by fading or impulse interference so that instead of several adjacent symbols being completely destroyed; many symbols are only slightly distorted.
This paper enhances the throughput of an existing OFDM system by implementing adaptive modulation and turbo cod- ing. The new system guarantees to reach a target performance BER of 10-2 over a slow time-varying fading channel. The sys- tem automatically switches from lower to higher modulation schemes on individual subcarriers, depending on the state of the quasi-stationary channel. In conjunction with the adaptive design, forward error correction is performed by using turbo codes. The combination of parallel concatenation and recursive decoding allows these codes to achieve near Shannon‘s limit performance in the turbo cliff region [2]. All this is simulated in MATLAB programming.


Orthogonal frequency division multiplexing (OFDM) is no- wadays widely used for achieving high data rates as well as combating multipath fading in wireless communications. In this multi-carrier modulation scheme data is transmitted by dividing a single wideband stream into several smaller or nar- rowband parallel bit streams.At the transmitter side, N sym- bols each representing m coded bits are mapped by an m -ary mapper and the output symbols are multiplexed into N paral- lel branches and modulated each by a subcarrier through the normal OFDM modulation (IFFT). The transmitter output con- sists of the superposition of N signals in the time domain. At the receiver, the received signal of a generic subcarrier after the FFT stage can be written as [2]:
r(n) = h(n)e(n) + w(n)
Where r(n), e(n), h(n) and w(n) are the received signal, trans-
mitted signal, complex flat-fading channel response and addi-
tive white Gaussian noise (AWGN) all at subcarrier (n), where
n = 1,2,…N , respectively. The channel is assumed to be per-
fectly known at all subcarrier positions. The data recover
process involves equalisation, demapping and decoding of the

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received signal. In this paper, the encoder and decoder are based on either a CTC or a BTC. Fig 1 shows the OFDM sys- tem architecture.


Turbo codes were first presented at the International Confe- rence on Communications in 1993. Until then, it was widely believed that to achieve near Shannon‘s bound performance, one would need to implement a decoder with infinite com- plexity or close. Parallel concatenated codes, as they are also known, can be implemented by using either block codes (PCBC) or convolutional codes (PCCC). PCCC resulted from the combination of three ideas that were known to all in the coding community:
The transforming of commonly used non-systematic convolu- tional codes into systematic convolutional codes
The utilization of soft input soft output decoding. Instead of using hard decisions, the decoder uses the probabilities of the received data to generate soft output which also contain in- formation about the degree of certainty of the output bits.
This is achieved by using an interleaver. Encoders and decod- ers working on permuted versions of the same information.
An iterative decoding algorithm centered around the last two concept would refine its output with each pass, thus resem- bling the turbo engine used in airplanes.

Fig. 2 Turbo encoder

The interleaved date sequence is passed to a seco nvolu- tional encoder ENC2, and a second coded bit stream, is gen- erated. The code sequence that is passed to the modulator for transmission is a multiplexed (an ssibly punctured) stream consisting of sys atic code bits and bits from both the first encoder and the second encoder .

3.2 Turbo decoding

A block diagram of a turbo decoder is shown in ―Figure 2‖. The

input to the turbo decoder is a sequence of received code values,

R { y s , y p }

from the demodulator [5]. The turbo decoder

Fig. 1. OFDM System Architecture

3.1 Turbo Encoding

The encoder for a turbo code is parallel concatenated convolu- tional code [3]. The block diagram of the encoder is shown in

―Figure 2‖. The binary input data sequence is represented by dk = (d1 , …….. dN). The input sequence is passed into the in- of a convolutional encoder. ENC1 and a coded bit stream,
is generated.
The data sequence is then interleaved. That is, the bits are loaded
into a matrix and read out in a way so as to spread the positions
of the input bits. The bits are often out in a pseudo-random man-

k k k

consists of two component decoder – DEC1 to decode sequences

from ENC1, and DEC2 to decode sequences from ENC2. Each of these decoders in a Maximum A Posteriori (MAP) decode EC1

takes as its input the received seque ystematic values and
the received sequence parity values belonging to the first en-

coder ENC1. The output of DEC1 is a sequence of soft estimates EXT1 of the transmitted data its . EXT1 is called extrinsic data, in that it does not contain any information which was given to DEC1

Fig3. Turbo decoder

DEC2 outputs a set of values, which, de-inter

by DEC2. This information is interleaved, and then passed to the second decoder DEC2. The interleaver is identical to that in the en-
coder (Figure1). DEC2 takes as its input the (interleaved) systematic

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rec values and the sequence of received parity val- ues from the second encoder ENC2, along with the interleaved form of the extrinsic information EXT1, provided by the first de- coder.
leaved using an inverse form of interleaver, constitute soft estimates EXT2 of the transmitted data sequence dk. This ex- trinsic data, formed without the aid of parity bits from the first code, is feedback DEC1. This procedure is repeated in iterative manner. The iterative decoding process adds greatly to the BER performance of turbo codes. However, after several itera- tions, the two decoders estimates of dk will tend to converge. If a set of corrupted code bits form a pair of error sequence that neither of the decoders is able to correct, then EXT1 and EXT2 may either diverge, or converge to an incorrect soft value. In the next sections, the algorithms used in the turbo decoding process, within DEC1 and DEC2.


The combination of turbo codes with the OFDM transmission is so called Turbo Coded OFDM (TC-OFDM) can yield signifi- cant improvements in terms of lower energy needed to trans- mit data, a very improvement issue is in personnel communi-

cation devices [1].

Fig 4. TCoded OFDM system

Fig 4 shows the simulation model for turbo coded OFDM that is used for implementing the various iterations. In the model shown in fig 4, A = turbo encoder, B = BPSK/QPSK modula- tion, C = serial to parallel converter, D = IFFT, E = parallel to serial converter, F = channel with noise, G = serial to parallel Converter, H = FFT, I = parallel to serial converter, J = BPSK/QPSK demodulation and K = turbo decoder.
For plotting the BER curves the different parameters are set for simulation.

4.1 Simulation Algorithm

The performance of the turbo coded OFDM has been meas- ured through MATLAB simulation. The simulation follows the procedure listed below:
1. Generate the information bits randomly.
2. Encode the information bits using a turbo encoder with the
specified generator matrix.
3. Use QPSK or different QAM modulation to convert the bi- nary bits, 0 and 1, into complex signals (before these modula- tion use zero padding)
4. Performed serial to parallel conversion.
5. Use IFFT to generate OFDM signals, zero padding is being
done before IFFT.
6. Use parallel to serial convertor to transmit signal serially.
7. Introduce noise to simulate channel errors. We assume that
the signals are transmitted over an AWGN (Additive White
Gaussian Noise) and Rayleigh channel.
8. At the receiver side, perform reverse operations to decode
the received sequence.
9. Count the number of erroneous bits by comparing the de- coded bit sequence with the original one.
10. Calculate the BER and plot it.

4.2 Simulation papramters




Digital Modula- tion


Turbo code rates


SISO Decoder


Code Generator

{111, 101}


pseudo random inter- leaver

Table 1 shows the various simulation parameters used in MATLAB. During the simulations, in order compare the re- sults, the same random messages were generated. For thet radiant function is in MATLAB.


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Fig 5: BER vs. SNR plot for uncoded and turbo coded

OFDM using BPSK and QPSK.

All the simulations are done to achieve a desired BER 10-3. For simulation results, two noise models were considered:
1. The AWGN and the time-Markov model. Both models are utilized by the parameters defined above.
2. The BER performance of TCOFDM system is compared with the respective uncoded system under the AWGN channel. No other channel codes are considered in this paper as the itera- tive decoding scheme easily outperforms conventional codes, or in other words non-iterative decoded codes.

In a multipath environment, it is reasonably spontaneous to visualize that an impulse transmitted from transmitter will reach the receiver as a train of impulses.The phase of each path can change by radian when the delay
changes by . If is large, relative small motions in the

medium can cause change of radians. Since the distance between the devices are much larger than the wavelength of the carrier frequency, it is reasonable to assume that the phase is uniformly distributed between 0 and radians

Fig 6. BER vs. SNR plot for turbo coded OFDM under one path rayleigh channel

and the phases of each path are independent. When there are large number of paths, applying Central Limit Theorem, each path can be modelled as circularly symmetric complex Gaussian random variable with time as the variable. This model is called Rayleigh fading channel model. The figure 6 shows the BER plot for turbo coded OFDM under one path rayleigh channel
Orthogonal frequency division multiplexing (OFDM) com- bines the advantage of high achievable rates and relatively easy implementation. In this their iscombined use of the turbo codes (TC) and the orthogonal frequency division multiplex-
ing in Rayleigh fading channel.

Fig 7. BER VS SNR plot for uncoded and coded OFDM

The system is called TC-OFDM with Rayleigh fading envi- ronment.The simulation results of TC-OFDM show that three iterations are sufficient to provide good BER performance. The figure 7 shows the gain of 5 dB at 10-5 in Rayleigh Fading channel is achieved.
All the simulations are done to achieve BER. For simulation results two channels are AWGN and RAYLEIGH are used. The BER performance of TCOFDM system is compared with uncoded OFDM system. As mentioned before, bursty errors deteriorate the performance of the any communications sys- tem. The burst errors can happen either by impulsive noise or by deep frequency fades.


[1] S. K. Chronopoulos, G. Tatsis, and P. Kostarakis (2011), ―Turbo

Codes―A New PCCC Design,‖ Communications and Network, Vol.

3, No. 4, 2011, pp. 229-234. doi:10.4236/cn.2011.34027

[2] M. K. Gupta and V. Sharma (2009), ―To Improve Bit Error Rate of Turbo Coded OFDM Transmission over Noisy Channel,‖ Journal of Theoretical and Applied Information Technology, Vol. 8, No. 2, 2009, pp. 162-168.

[3] Pfletschinger, S.(2007), ―Frequency-Selective Link Adaptation using Duo-Binary Turbo Codes in OFDM Systems‖ in proceedings of Mo- bile and Wireless Communications Summit, pp1-5.

[4] Liu Na Shi Wenxiao Wu Jiang(2006), ―A Model of Turbo Code Based

on OFDM-CDMA‖ in IEEE journal.

[5] Wang, Xiaodang (2005). OFDM and its application to 4G, In: 14th Annual conference on wireless and optical communications, USA, p.69-71.

[6] L. Hanzo, T. Keller(2003), ―OFDM & MC-CDMA for Broadband Mul- tiuser Communications, WLANs and Broadcasting‖ John Wiley Pu b- lishers.

[7] Cimini, L.J., Jr., Chuang, J.C.(2002), ―Comparison of convolutional

and turbo codes for OFDM with antenna diversity in high-bit-rate

wireless applications‖, IEEE Communication letters, Vol4, issue 9, pp

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[8] G. Burr, G. P. White (1999) "Performance of Turbo-coded OFDM" in lEE Trans. Of International Conference on Universal Personal Com- munications.

[9] W. J. Blackert, S. G.Wilson (1995), "Turbo Code Termination and

Interleaver Conditions", lEE Electronics Letters, val. 31, no. 24, pp.


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