SIMULATIONS OF ERROR CORRECTION CODES FOR DATA COMMUNICATION OVER POWER LINES

SIMULATIONS OF ERROR CORRECTION CODES FOR DATA COMMUNICATION OVER POWER LINES Michelle Foltran Miranda Eduardo Parente Ribeiro mifoltran@hotmail.com edu@eletrica.ufpr.br Departament of Electrical Engineering, Federal University of Parana Centro Politécnico CP 19011, CEP 81531-990, Curitiba - PR Brazil Walter Godoy Jr. godoy@cefetpr.br Federal Center of Technological Education of Parana CEFET Curitiba - PR Brazil Abstract. The main contribution of this article is to describe the implementation of a simulation environment to verify the performance of error correction codes in Orthogonal Frequency Division Multiplexing (OFDM) systems for data communication on a power line noise channel. Monte Carlo simulation was used to evaluate convolutional codes, Reed- Solomon codes and turbo codes on additive white gaussian noise (AWGN) and on a measured power line noise. Adequate models for power line channel have not been established, therefore the chosen approach was to compare the results obtained with simulations using measured power line noise. Keywords: OFDM, error correction code, turbo code, noise, power line communication

1. INTRODUCTION Power lines can be found in essentially all buildings and residences and are considered a convenient and inexpensive medium for data communication. In areas where telephone, cable or wireless solutions do not reach, power line communication (PLC) forms the only feasible solution. Although power lines are an attractive medium, there are some difficulties in designing a system for data transmission. One of the problems faced by PLC systems is the excessive amount of radiated interference. This could be mitigated by reducing transmitted signal power at the expense of reducing signal-to-noise ratio (SNR), which leads to an increase of bit error rate (BER). There comes the importance of choosing good forward error correction (FEC) codes, whose performances are well known for AWGN channels. However, the same does not occur for power lines. Due to the time-varying characteristics of this hostile channel, a precise model for PLC is not available yet (Biglieri, 2003). Therefore, designing a system for data transmission over the PLC is a challenging problem. This work compares the performances of some error correction codes in a simulated environment using real samples of measured power line noise. OFDM technique (Nee and Prasad, 2000) is considered and Monte Carlo method is used to estimate BER versus SNR of a certain error correction code for PLC channel. Convolutional code, Reed-Solomon code and turbo code (Berrou et al., 1993; Lauer and Cioffi, 1998; Zhang and Yongacoglu, 2001) are investigated. Their performances for AWGN channel have also been plotted for comparison purposes. Those error correcting codes can be used in various applications. In Discrete Multitone (DMT) technique used in Asymmetric Digital Subscriber Lines (ADSL) (Kallet, 1999), Reed-Solomon codes are required and convolutional codes can optionally be applied. Turbo codes are a new class of convolutional codes whose performance in terms of bit error rate is close to the Shannon limit. The encoder is built with a parallel concatenation of two recursive systematic convolutional codes and an iterative method is used for decoding. In this paper, OFDM transmission systems without coding and with convolutional, Reed- Solomon and turbo coding are described in section 2, which also presents the simulation methodology. Sections 3 presents the results for AWGN channel and for measured power line noise. The conclusion is given in section 4. 2. METHODOLOGY Monte Carlo method is adopted in simulations to estimate the system performances for AWGN and PLC channels. Before describing the simulation used to obtain the results, it is necessary to present a brief review of the OFDM transmission systems with and without coding. 2.1 OFDM Transmission System In an OFDM transmission system, as shown in Fig. 1, input bits are allocated into N subchannels and are mapped into complex QAM symbols. These complex values with their conjugate symmetric vector are the inputs to the IFFT operator, forming 2N values. The output is converted into a continuous signal by a digital-to-analog conversor (D/A) for transmission through the channel. During transmission, noise will be added to the signal, which will cause errors in the system. In the simulations, 256 subchannels are considered and 4 input bits (b i, where i indicates the number of the subchannel) are allocated to each subchannel. A 16-QAM mapper and an IFFT operator of length 512 are adopted. Figure 2 shows the receiver block diagram. After analog-to-digital conversion (A/D), the received

signal enters the FFT operator, yielding Y i complex values. Then, the resulting signal is converted into bits by the QAM demappers and are fed into a parallel-to-serial conversor. 2.2. Reed Solomon Codes in OFDM Systems Reed-Solomon codes are nonbinary BCH codes used in various applications. In ADSL, RS codes over GF(256) are recommended, i. e. each code symbol is one byte. A RS code of block length n and number of information symbols k is denoted as RS(n,k). It has a redundancy of r=n k and can correct up to t symbol errors, where r = 2t. In the simulations presented in this paper, the code C(255,216) over GF(256) is used (Zhang and Yongacoglu, 2000) and a hard decision decoding is performed. The transmission system is illustrated in Fig. 3. Information bits are fed into the RS encoder and the coded output is grouped and divided into 256 subchannels (N). For 16-QAM, 4 bits are allocated to each subchannel b i (i=1..n). Then, a natural QAM mapping is performed on this subchannels, forming X i complex symbols. The result is fed into an IFFT operator of length 512. Figure 4 shows the scheme for RS decoder. In the receiver, FFT is performed and the Y i QAM symbols are demapped. Bits in each subchannel (b i ) are the input to a parallel-to-serial conversor and then are fed to the RS decoder. Figure 1 - OFDM transmission system without coding Figure 2 - OFDM receiver system without coding Figure 3: RS Encoder in OFDM system

2.3. Convolutional Codes in OFDM Systems Figure 4. RS Decoder in OFDM system An alternative to trellis coding is to use a binary convolutional code together with a nonbinary modulation scheme, as QAM (Wang and Onetera, 1995; Nee and Prasad, 2000). Binary input data are converted into QAM symbols according to a Gray code mapping. For the case of 16-QAM, the in-phase and quadrature components are treated separately as 4 level PAM values, determined by bits b0 and b1, as shown in figure 5. The vertical lines indicate the regions in which the bit values are 1. For instance, if bits 1011 are allocated to a certain subchannel, Gray mapper should map the firt two bits (10) into +3 and the last ones (11) into +1, forming the complex symbol 3+j. At the receiver, the QAM symbols must be demmaped into two one-dimensional values with corresponding metrics which will be quantized into 8 levels and are the input to the Viterbi decoder. For 16-QAM, the in-phase and quadrature values are treated as independent 4 level PAM signals, which are demapped into two metrics as shown in figure 6. Assume the complex symbol 3+j is received. The real part must produce two metrics according to the traces in figure 6. In this case, it is demapped into two values: +3 and -1. The imaginary part also produces two values: +1 and +1. In this simulation, a convolutional code of rate ½, constraint length 7 and vector generator g=[133,171] is adopted. This code is one of the most utilized as remarked by Nee and Prasad (2000). Figure 7 shows the scheme for transmission. The input bits are encoded by the convolutional encoder, and then grouped and divided into 256 subchannels, forming 4 bits (b i ) in each subchannel. These bits enter a Gray mapper, resulting in complex symbols (X i ) that are fed to an IFFT operator of length 512 and then transmitted to the channel. The received signal is the input to a FFT operator, as shown in Fig. 8. The complex symbols (Y i ) are then separated in in-phase and quadrature components and are treated independently to produce the binary metrics for Viterbi decoder. In the case of 16-QAM, 4 metrics are obtained. These metrics are quantized into 3 bit level and are the input to the binary Viterbi decoder, which produces a soft decision of the information bits. Figure 5. Gray Mapping of two bits into 4 level PAM

Fig. 6. Demapping of 4 level PAM into 2 metrics Fig. 7. Convolutional encoder in OFDM system 2.4 Turbo Codes in OFDM Systems Fig. 8. Convolutional decoder in OFDM system Turbo codes have been shown to provide near Shannon limit performance in AWGN channels. A standard binary turbo encoder consists of two recursive systematic convolutional codes (RSC) separated by an interleaver. A decoding algorithm maximum a posteriori (MAP) is adopted as an iterative method to produce a better performance. In this paper, a binary turbo code of rate ½ and vector generator g=[11111; 10001] is used to encode the information bits. The number of iterations used was 3 and represents a compromise between the quality (less error) and speed. Bandwidth efficient turbo trellis coded modulation schemes have been investigated in literature (Goff et al., 1994; Robertson and Wörz, 1996). In these publications, turbo codes are combined with QAM modulation and provide near Shannon limit performance. Turbo codes can also be applied to DMT systems (Lauer and Cioffi, 1998; Zhang and Yongacoglu, 2001). Figure 9 shows the encoder structure. The turbo code outputs are demultiplexed and separated into systematic and parity components. A puncturing function (P) is inserted to obtain a large

code family, with various rates R. In the present simulation, puncturing has been used to obtain a code rate of ½ by transmitting the systematic information and the odd check bit from RSC1 and then the next systematic information and the even check bit from RSC2. In order to obtain uncorrelated symbols, bits pass by an interleaver (I). In this paper, a pseudo-randomic interleaver of length 512 is assumed. These bits are then allocated into 256 subchannels, each one with 4 bits. A Gray mapping is then performed and the symbols are the inputs to the IFFT operator of length 512. At the receiver, as in Fig. 10, the FFT is performed and the receiver block calculates the previously presented metrics that represent the a posteriori log-likelihood (LLR) of the received symbols. Then, the LLRs (?) pass by a de-interleaver (I-1), are demultiplexed and used as the inputs to the binary turbo decoder that uses a MAP algorithm to perform the decoding (Goff et al., 1994). Fig. 9. Turbo encoder in OFDM system Fig. 10. Turbo decoder in OFDM system 2.5. Simulations The transmission system simulation has been implemented in Matlab. Two communication system channels have been considered: an additive white gaussian noise (AWGN) channel and an additive noise channel using a measured noise at the power outlet in the laboratory. A power line channel model has not been established yet, although there are some publications about the theme (Marubayashi and Tachikawa, 1996). There are various problems which increase this modelling dificulty (Biglieri, 2003): frequency-varying and time-varying attenuation of the medium, dependence of the channel model on location, network topology and connected loads, high interferences due to noisy loads, high nonwhite background noise and impulse noise. In this work, only the interference noise has been considered and the system transfer function has been supposed an all-pass. Then, the effect of noise on different error correcting codes could be isolated permitting a controlled comparison. Measurements have been made to obtain real samples of power line noise. A 12-bit analog-to-

digital (A/D) converter with sampling rate of 40 ksps has been used to obtain 60000 samples from the power line. Analog high-pass filter with cutoff frequency of 200Hz and an antialiasing (low-pass) filter at 20 khz were used. Two other measurements have been made by adding a sinusoidal interference at the frequency of 19kHz, with amplitude of 1V and 6V inserted by a signal generator coupled with a transformer. The uncoded and coded (convolutional, RS and turbo code) systems have been simulated and their performances have been evaluated for the case of an AWGN channel for OFDM modulation with 16-QAM. In a second stage, these same systems have been submitted to a measured power line noise with and without the interference of 19kHz. In that case, a transmission starting from 10 khz has been considered. A digital high-pass filter with cutoff frequency in 6 khz has been inserted in the receiver to eliminate remains of 60 Hz and its harmonics. The curves of the bit error rate (BER) as a function of signal-to-noise ratio have been plotted using the Monte Carlo method. The input data for simulation is the signal-tonoise ratio obtained by the power ratio of the transmission signal and of the noise signal. As result, BER is calculated for transmissions until 500 bit errors. Fig.11. System performances on AWGN channel Figure 12: Power spectral density of measured power line noise and generated gaussian pseudo-noise.

3. Results Figure 11 shows the bit error rate as a function of the signal-to-noise ratio E b /N 0 for OFDM systems with 16-QAM in the simulated AWGN channel, where E b is the energy received per information bit and N 0 is the noise monolateral power spectral density. This simulated curve is verified to be in agreement with the theoretical formulation. The turbo code superiority is observed in AWGN channels. For 16-QAM, the turbo coded system presents a better performance when compared to the others. At a BER of 10-6, the turbo coding gain compared to that produced by the Reed-Solomon code is 7 db. When compared to the convolutional code, the coding gain is 2 db. In a second stage, the same coded and uncoded systems have been submitted to a measured power line noise from the outlet of the laboratory (Curitiba, Brazil). Figure 12 shows the power spectral density of the measured power line noise and gaussian white pseudo-noise with the same power (both high-pass filtered at 6 khz). While white noise exhibits flat amplitudes along the frequencies, measured power line noise contains interferences, non-white noise and impulse noise. Fig. 13. System performances for OFDM with 16-QAM and 256 subcarriers on PLC channel Fig. 14. System performances for OFDM with 16-QAM and 256 subcarriers for convolutional code

Figure 13 shows the system pexformances for measured PLC noise. The turbo code maintains a superior performance when compared to the uncoded system and presents better results than the convolutional code and the Reed-Solomon code. In that case, at a BER equal to 10-6, the coding gain is 6 db when compared to the Reed-Solomon code and 2 db when compared to the convolutional code. It can be noticed that for the power line channel, the coding gain is smaller than that for the AWGN channel. Figure 14 exhibits a comparison of the convolutional code performance on the AWGN channel and on the measured power line noise with and without the interference signal of 1V and 6V. As voltage increases, the system performance on power line noise becomes worse. It can be noticed that the difference in bit signal-to-noise ratio for the AWGN channel at a BER equal to 10-5 is 1dB compared to that for power line noise. Indeed, the AWGN channel is not considered a good model for PLC. Fig. 15. System performances for OFDM with 16-QAM and 256 subcarriers for turbo code Fig. 16. System performances for OFDM with 16-QAM and 256 subcarriers for Reed- Solomon code Figure 15 shows a comparison between the AWGN channel and the power line noise for the turbo coded system. System performances are about the same up to 3dB (Eb/No), but for greater relations AWGN presents fewer errors. Figure 16 compares the system on AWGN and

on power line noise for the Reed-Solomon code. In that case, the curves of bit error rate were very close. 4. CONCLUSION An environment for simulating data transmission in OFDM over noisy channel has been implemented and tested. The simulated result for AWGN was in accordance with theoretical formulation. The performances of the Reed-Solomon code, the convolutional code and the turbo code have been verified for data transmission in an AWGN channel and on a measured power line noise channel. Results show that the codes perform differently on real noise compared to additive white gaussian noise. Such difference can be explained by the high interferences, high nonwhite background noise and impulse noise present in PLC channel. It confirms that a careful choice of code is very important for best performances and that an analysis on a more realistic scenario is necessary. For turbo and convolutional codes, the performances on PLC showed a difference of 1,5 db for a BER of 10-6 when compared to the AWGN channel. For the Reed-Solomon code, such difference has been smaller and inferior to 0,2 db. The turbo code superiority compared to the other coded and uncoded systems has been verified for AWGN channel and for the studied power line noise, presenting a gain of about 2 db when compared to the convolutional code of the same rate. It is interesting to observe that the coding gains introduced by the turbo, convolutional and Reed-Solomon codes have always been superior under AWGN channel. It can be noticed that the AWGN model produces better results than that obtained with the measured power line noise and is not an adequate model in this case. This methodology could also be extended to higher frequency ranges (MHz), allowing the evaluation of the same modulation and error correction schemes in a different range where the noise may have diverse characteristics. Acknowledgments We would like to thank Dr. Weiler Finamore for bringing us the topic of turbo codes and for helpful discussions. REFERENCES Berrou C., Glavieux A., & Thitimajshima P., 1993. Near Shannon Limit Error-correcting Coding and Decoding: Turbo Codes, IEEE International Conference on Communications., vol. 2, pp.1064-1070. Biglieri, E., 2003. Coding and Modulation for a Horrible Channel, IEEE Communication Magazine, Vol. 41, pp. 92-98. Goff, S. Le, Glavieux A., & Berrou C., 1994. Turbo Codes and High Spectral Efficiency Modulation, IEEE Transactions Communications, vol. 2, pp. 645-649. Kallet, I., 1989. The Multitone Channel, IEEE Transactions Communications, Lauer, J. P., & Cioffi, J. M., 1998. Turbo Coding for Discrete Multitone Transmission Systems, IEEE Transactions Communications. Marubayashi, G., & Tachikawa, S.,1996. Spread Spectrum Transmission on Residential Power Line, IEEE 4th International Symposium on Spread Spectrum Techniques and Applications Proceedings, vol. 3, p. 22-25.

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