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B. Fong et al.: Forward Error Correction with Reed-Solomon Codes for Wearable Computers 917 Forward Error Correction with Reed-Solomon Codes for Wearable Computers B. Fong, Senior Member, IEEE, P. B. Rapajic, Senior Member, IEEE, G. Y. Hong, Member, IEEE, and A. C. M. Fong, Member, IEEE Abstract — High-speed multimedia data transmission is vulnerable to burst errors primarily due to its frame structure. Forward error correction (FEC) codes mitigate the effects of multipath fading as some form of time diversity by adding redundancies into the transmitted data. This paper evaluates the performance of Reed-Solomon codes on transmitting ATM data for lightweight wearable computers using single carrier modulation. The aim is to maximize link availability and minimize the impact of atmospheric conditions on bit error rate (BER) performance. The performance is compared with signals transmitted without any forward error correction scheme. This scheme is particularly suitable for small wearable computers with high portability due to simplicity of circuitry making it suitable for consumers on the move. Index Terms — Burst error, Link availability, Singlecarrier Modulation, Wearable computers. I. INTRODUCTION HIGH speed wireless Asynchronous Transfer Mode (ATM) networks are widely used for multicast distribution of multimedia data over a locality. Microwave links that carry the data suffer from fading due to rain attenuation, depolarization, multipath, and frequency fading [1]. The quality of service (QoS) of a wireless network is largely dependent on maximizing the link availability between the basestation modem unit (BMU) and the customer-premises equipment (CPE). Wearable computers are found appealing in the ever growing consumer electronics industry as multimedia service enhancements make small devices such as PDA (personal digital assistant) and WAP (Wireless Application Protocol) compatible cellular phones are able to provide a range of network services for subscribers on the move. A number of challenges exist for reliable operation of wearable computers in an outdoor environment particularly under the influence of heavy and persistent rainfall [2]. The need for reliable error correction is therefore crucial for maximizing system QoS to ensure adequate network availability. B. Fong is with Auckland University of Technology, Private Bag 92006, Auckland 1020, New Zealand (e-mail: bfong@ieee.org) P.B. Rapajic is with School of Electrical Engineering and Telecommunications University of New South Wales, Sydney 2052, Australia. G. Y. Hong is with Massey University- Albany Campus, Private Bag 102904, North Shore Mail Center, Auckland, New Zealand A. C. M. Fong is School of Computer Engineering, Nanyang Technological University, Singapore Earlier research [3], [4] have found that Reed-Solomon codes (R-S) are effective in minimizing the impairment caused by burst errors in delivery of high speed data traffic, which is the most significant type of error associated with ATM multimedia traffic because of its data frame structure. A reduction in the bit error rate (BER) can be realized by FEC, this consequently leads to an increase in microwave link availability in the expense of slightly lowering the effective available bandwidth due to redundancies. FEC codes have been widely used in consumer electronics equipment such as audio compact discs (CD) [5] and random access memory (RAM) [6]. Earlier work on applying FEC to broadband networks have been performed by [7], [8]. Results show that FEC is generally effective when there is a high degree of correlation in the error and its performance is largely dependent on the spread of error. Our work seeks to evaluate the performance of R-S code on the improvement for delivering ATM traffic to mobile receivers. The link availability is measured by the percentage of time in which it can provide a BER of 10-6 or better. Factors that affect the link performance that ultimately determines the maximum coverage range are mainly due to geographical conditions with both stationary and moving obstacles causing signal degradation due to phenomena such as shadowing, multipath, and environmental conditions resulting from rain and snow. Improvement in the link BER performance by using R-S encoding has been studied in this paper. II. PROBLEM STATEMENT Wireless links are harsh environments for data transmission due to conditions such as multipath fading and attenuation. Wideband communication is particularly vulnerable to such signal degradation. It is also realized that most of the error involved is burst errors in multimedia traffic. Overheads for FEC can be added to data frames to improve QoS as a result of BER improvement. Frame relay networks are susceptible to burst errors. While the IEEE 802.11 standard provides specifications on wireless networks, it does not specify the type of modulation scheme and error correction mechanism for deployment as there is no single optimal solution that offers best performance. Rain causes scattering, depolarization and phase rotation to radio waves. Highly robust error correction is important in ensure maximum reliability for wearable computers with high mobility in an outdoor environment. Contributed Paper Manuscript received May 15, 2003 0098 3063/00 $10.00 © 2003 IEEE 918 IEEE Transactions on Consumer Electronics, Vol. 49, No. 4, NOVEMBER 2003 ATM Network Backbone DS3 E3 Radio hub Line-of-Sight 12 Mbps SubscriberInternalEnd-user Access connection node System Fig. 1 System Layout for providing multimedia services to wearable computers Multimedia S/P data Ts 2 R-S Encoder R-S Encoder Filter e I(t) u (t) I Cross fc correlator Q(t) o 90 Σ u (t) Q Filter e Fig. 2 Encoding mechanism III. SYSTEM LAYOUT A wireless local area network (WLAN) system operating at a carrier frequency of 5 GHz has been used. This system offers distinctive advantages in network capacity [9]. The system block diagram is shown in Fig. 1. This system consists of three main parts, Switching that connects the access system to its network backbone using a fixed E3 connection via the radio hub. The Transport segment relays data to the BMU where data is transmitted over the link. The Access part is a subscriber radio unit and a subscriber access system which process the received data and the data is then collected for a notebook computer to perform data analysis. The objective is to improve the tolerance to burst error with wearable nodes.An outdoor line-of-sight (LOS) link is established between the antennas of the transmitter and the receiver. The link is evaluated under conditions when persistent heavy rainfall causes maximum degradation to the link performance in a tropical region of ITU-P [10]. The maximum range of the microwave link as a function of the percentage of time that the link maintains a BER of no worse than 10-6 is shown in Fig. 3. The main causes of link outage are due to weather conditions such as rain and fog. Such effects can usually be compensated by adjustment made to the fade margin. The result shown indicates the maximum link range for a transmission rate of 12 Mbps using a 5 GHz carrier with LOS and no rainfall. The range for 99.99% availability is 18 km. Each ATM cell consists of only 8 error checking header bits. Any cell that is received with an error Fig. 3 Maximum link coverage not corrected by the FEC is relayed to the subscriber access system with the error still present. The system performance is also largely determined by its modulation scheme. While there are a number of options available depending on factors such as bandwidth efficiency, transmission power and cell-to-cell interference. Multicarrier modulation offer a number of advantages for wireless multimedia transmission as described in [11], single carrier modulation schemes is selected for their high level of narrowband noise immunity due to inherent capability by use of adaptive equalization and reduced receiver structure B. Fong et al.: Forward Error Correction with Reed-Solomon Codes for Wearable Computers 919 complexity because of simplified decoding mechanism with the added advantage of being more tolerant to noise and interference. The system is set up to evaluate the effects of ReedSolomon codes on the radio link availability as shown in Fig. 1. Forward Error Correction (FEC) technique provides a means to reduce the BER. Data frames are sent across an LOS radio link supporting a data rate of 12 Mbps. The data is transmitted using QPSK modulation for its robustness and relatively good tolerance to noise and interference with ease of implementation [12]. Fig. 2 shows the structure of transmitter with R-S encoding mechanism. The symbol sequence polynomial is given by a( x) = ak−1x k−1 + ak−2 x k−2 + ... + a1x + a0 (1) The code words are encoded using the product of the generator polynomial g(x) and the information block such that: TABLE I THE GF(2M) R-S CODES Field GF( ) R-S Code 2m 16 32 64 128 256 Where k is chosen as 8 bit. (N= 2m –1, k, d= 2m -k) (15, 8, 8) (31, 8, 24) (63, 8, 56) (127, 8, 120) (255, 8, 248) v( x) = v0 + v1x + ... + vn−1x n−1 (6) whereas the information polynomial can be represented as u( x) = u0 + u1x + ... + uk−1xk−1 (7) This information polynomial can be transformed as the code polynomial v(x) with the generator polynomial 15 g(x) = ∏ (x − ai ) i=0 15 ∑ g(x) = x16 + gi xi i=0 (2) gt (x) = LCM [φi (x)] 1 ≤ i ≤ 2t v(x) = xn−ku(x) + xn−ku(x)gt (x) (8) (3) where xn-k u(x) is divided by gt(x) to obtain the remainder xn-k u(x) gt(x). For an RS(n,k) code with symbols from GF(2m), there will be an m2 number of cells. The codes of GF(2m) are listed in Table 1. IV. DECODING ALGORITHM A burst erasure correction R-S code [7] is used for FEC. The notation RS(N,k) represents a code block of N symbols length that contains k information symbols. This code is defined in a Galois field as GF(2m) where m represents the bit length of a code symbol. With an N point GF DFT defined as ∑ Vk = N −1 viα ik (4) k =0 b. Rate of erroneous correction The network delivers a range of data from different multimedia applications such as audio and video data. In our system, bulk data transfer with a single burst source of a fixed number of cells is used for ease of implementation. The burst error received is fed into the R-S decoder for burst correction. The probability of incorrectly manipulating the burst error with a burst of length exceeding 16 is shown in Fig. 4. ∑ vi = α V N −1 −ik k (5) k =0 where a primitive N-root of α is the kernel. By solving these equations in the frequency domain that yields an error locator polynomial having a root of α-i, an error occurs at position i of the received data block. a. Reed-Solomon Coding GF(2m) denotes the finite field of 2m elements with n defined as (2m -1). An RS(63, 56) code has 63 code symbols and 56 information symbols in each block with 8 bits. The code symbols can be represented as the coefficients of code polynomial Fig. 4 Probability of correction error 920 IEEE Transactions on Consumer Electronics, Vol. 49, No. 4, NOVEMBER 2003 c. Over radio channels The radio channel is assumed to be slow fading with the signal of the forward channel defined as a Rayleigh random variable with pdf p(a) = 2a. exp(−a 2 ) (9) It is assumed that the channel is not frequency-selective and the effects of signal degradation caused by multipath fading is eliminated by using an equalization method as described in [13]. A code symbol error occurs when there is a code symbol that is failed to be detected as an erasure. The received symbol that contains errors can be represented by r(a) = s(a) + e(a) = 15 ∑ ria i (10) i=0 corrected. Such cut off is performed manually at the receiving end. A comparison between no error correcting mechanism and the deployment of FEC codes has been made over the same microwave link under identical operating environments. The system’s Eb/No performance is shown in Fig. 6 without error correction. The BER performance with an 8% overhead of check bits are measured and results are shown in Fig. 7. The insertion of Reed-Solomon FEC codes yields an improvement on the link availability at the expense of a marginal increase in data rate due to redundancies. The results show that at BER = 10–6, when the link is at the boundary of barely available, the Eb/No ratio with FEC is increased by 4 dB. The improvement is even more significant as the BER further decreases. where s and e denote the transmitted signal and error as a function of a, respectively. This yields to the syndrome polynomial coefficients as Si (a) = r(ai ) = s(ai ) + e(ai ) 1 ≤ i ≤ 2t (11) The processing time of the R-S decoder is show in Fig. 5 where it is noted that the decoding time for up to a burst length of 30 symbols is acceptable that takes less than 450 machine clock cycles to complete. Fig. 6 System performance Fig. 5 Processing time of R-S decoder with burst length between 15 and 30 symbols. Fig. 7 Performance of Reed-Solomon FEC codes V. RESULTS Multimedia traffic is transmitted over the link as described in Section II above and the received data is collected for data analysis. The receiver is suspended whenever the link is unavailable, that is, when its BER falls below 10-6. This is because even with FEC, large amount of errors cannot be It is also noted from Fig. 7 that the rate of Eb/No improvement with FEC is significantly reduced due to the much steeper slope of the performance curve. This means that a small change in Eb/No causes very high fluctuation of BER. As a result, the link availability will be changed between available and unavailable much more frequently than in the case where no error correcting mechanism is used. B. Fong et al.: Forward Error Correction with Reed-Solomon Codes for Wearable Computers 921 VI. CONCLUSIONS This paper presents the performance of Reed-Solomon codes for error correction in wearable computers. The harsh operating environment of small wearable computers in the open is particularly vulnerable to transmission error. ATM traffic is susceptible to burst errors and the effects of performance degradation can be compensated by the use of Reed-Solomon codes for error correction. A slight increase in data rate due to 8% overhead yields a noticeable improvement in BER performance that consequently leads to a higher availability of the radio link as a minimum BER of 10-6 can be attained at a much lower Eb/No. Results with QPSK show that Eb/No is dropped from 11.2 dB to 7.3 dB when the link is barely available. A further improvement is noted when the BER is lowered to 10-8 where the difference of almost 5 dB in Eb/No is offered by FEC. It is shown that although FEC is unable to fully correct errors due to burst errors, it does offer a significant improvement on the link availability. Bernard Fong (M’93) graduated in Electrical Engineering from the University of Manchester (UMIST), United Kingdom. He is currently a faculty member in telecommunication engineering and multimedia with the Department of Electrotechnology, Auckland University of Technology, New Zealand He was previously a Staff Engineer with HewlettPackard. His research interests include wireless communications, Internet technologies and engineering project management. Predrag B. Rapajic (M’89-SM’99) received the B.E degree from the University of Banja Luka, Yugoslavia, in 1982, and the M. E. degree from The University of Belgrade, Belgrade, Yugoslavia, in 1988. He received the Ph.D. degree from The University of Sydney, Sydney, Australia in 1994. In 1996, he was appointed Head of the Communications Group, Motorola Australian Research Center. Since 2000, he has been a Senior Lecturer at The University of New South Wales, Sydney, Australia. His research interests include adaptive multiuser detection, equalization, error control coding, mobile communication systems and multiuser information theory. REFERENCES [1] B. Fong, P. B. Rapajic, A. C. M. Fong, and G. Y. Hong, “Polarization of received signals for wideband wireless communications in a heavy rainfall region”, IEEE Communications Letters, Vol. 7 No. 1, January 2003, pp. 13- 14 [2] B. Fong, P. B. Rapajic, G. Y. Hong, and A. C. M. Fong, “Factors Causing Uncertainties in Outdoor Wireless Wearable Communications”, to appear in IEEE Pervasive Computing, Vol. 2 No. 2, April 2003. [3] J. Chen and P. Owsley, “A Burst-Error-Correcting Algorithm for ReedSolomon Codes”, IEEE Transactions on Information Theory, Vol. 38 No. 6, Nov 1992, pp. 1807- 1812 [4] L. Yin, J. Lu, K. Ben Letaief and Y. Wu, "Burst-error correcting algorithm for Reed-Solomon codes", Electronics Letters, Vol. 37 No. 11, May 25, 2001, pp. 695- 697 [5] L. B. Vries and K. Odaka, "CIRC- The error correcting code for the compact disc", AES Premier Conference, June 1982 [6] S. Kaneda and E. Fujiwara. "Single bit error correcting double bit error detecting codes for memory systems", IEEE Transactions on Computer, Vol. C-31, July 1982, pp. 596- 602 [7] A. J. McAuley, "Reliable broadband communications using a burst erasure correcting code", Conference Proceedings of ACM SIGCOMM, September 1990, pp. 287- 306 [8] E. W. Biersack, "Performance evaluation of forward error correction in an ATM environment", IEEE Journal on Selected Areas in Communications, Vol. 11 No. 4, May 1993, pp. 631- 640 [9] B. Fong and G. Y. Hong, "RF net scales broadband to local area", EE Times, June 17, 2002. [10] “ITU-R recommendations”, P-ser, Rec. ITU-R P. 618-5 [11] M. Rohling, T. May, K. Bruninghaus, and R. Grunheid, “Broad-band OFDM radio transmission for multimedia applications”, Proceedings of the IEEE, Vol. 87 No. 10, October 1999, pp. 1778- 1789 [12] B. Fong, G. Y. Hong, and A. C. M. Fong, “A modulation scheme for broadband wireless access in high capacity networks”, IEEE Transactions on Consumer Electronics, Vol. 48 No. 3, pp. 457-462, August 2002. [13] D. K. Borah and P. B. Rapajic, "Optimal adaptive multiuser detection in unknown multipath channels", IEEE Journal on Selected Areas in Communications, Vol. 19 No. 6, pp. 1115-1127, June 2001. G. Y. Hong (M’95) received her Ph.D. degree from the National University of Singapore. She is currently with Massey University (Albany Campus). A. C. M. Fong received his degrees from the University of Auckland and Imperial College, London. He is currently an Assistant Professor in Computer Engineering at Nanyang Technological University. His research interests include various aspects of Internettechnology, information theory, and video and image signal processing. He is a Chartered Engineer.

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