SIMULATIONS OF ERROR CORRECTION CODES FOR DATA COMMUNICATION OVER POWER LINES Michelle Foltran Miranda Eduardo Parente Ribeiro [email protected] [email protected] Departament of Electrical Engineering, Federal University of Parana Centro Politécnico CP 19011, CEP 81531-990, Curitiba - PR – Brazil Walter Godoy Jr. [email protected] 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 (bi, 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 Yi 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 bi (i=1..N). Then, a natural QAM mapping is performed on this subchannels, forming Xi 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 Yi QAM symbols are demapped. Bits in each subchannel (bi) 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 Figure 4. RS Decoder in OFDM system 2.3. Convolutional Codes in OFDM Systems 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 (bi) in each subchannel. These bits enter a Gray mapper, resulting in complex symbols (Xi) 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 (Yi) 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 Fig. 8. Convolutional decoder in OFDM system 2.4 Turbo Codes in OFDM Systems 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.