ADAPTIVE ITERATION SCHEME OF TURBO CODE USING HYSTERESIS CONTROL

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1 ADATIV ITRATION SCHM OF TURBO COD USING HYSTRSIS CONTROL Chih-Hao WU, Kenichi ITO, Yung-Liang HUANG, Takuro SATO Received October 9, 4 Turbo code, because of its remarkabe coding performance, wi be popuar for the next generation wireess communication systems. This paper assesses the performance of an adaptive iteration agorithm for turbo decoding in AWGN. Numerica resuts are presented to demonstrate the feasibiity of the agorithm.. Key words: Turbo decoding, Adaptive iterations, Hysteresis contro Turbo coding [] [] architectures ie at the heart of a third-generation (3G) wireess standards, incuding UMTS [3] [4] and CDMA [5]. These types of coding are caed for because they aow systems to meet the tough bit-error-rate (BR) requirement and ow signa-to-noise ratios (SNR) paced on emerging 3G designs. The optimum decoding of turbo codes is the maximum ikeihood-decoding agorithm appied to the turbo code treis structure [6]. However, due to the intereaver embedded in the turbo encoder, the turbo code treis wi have an extremey arge number of states. This fact makes the maximum ikeihood decoding process amost impossibe to impement in practice for arge intereaver sizes. A more practica approach is an iterative decoding approach by which the maximum ikeihood decoding agorithm is appied to the eementary convoutiona /bock codes of the turbo code. This iterative process raises the question of how cose its performance is to the performance of the optimum decoding process. In [], it was shown that turbo codes are near optima codes. Simuation resuts based on an iterative decoding approach were within.7 db of the sphere packing ower bound for various code rates and an information bock size from to, bits. Therefore, this iterative technique is a very efficient way to decode turbo codes and to achieve performance cose to the theoretica imits. However, caing for turbo coding architectures and actuay impementing them are words apart. Turbo codes deiver exceent BR and SNR performance. But these achievements come at the cost of intense computing requirements. At a high data rate, the turbo decoder aone may consume more power than the rest of the base band transceiver [7] [8]. Liteon Technoogy Wireess Research and Design Department Department of Information and ectronics ngineering, Associate rofessor Waseda University, rofessor

2 In the ast decade, both mobie communications and mutimedia communications have experienced unequaed rapid growth and commercia success. Naturay, the great abeit separate successes in these areas fue the od vision of ubiquitous mutimedia communication enabing the user to communicate from anywhere at any time, transmitting and receiving any type of data. The convergence of mobie and mutimedia venues is now underway. In the future, video and image transmission wi become very important for ceuar systems and wireess LAN systems. The wireess environment is in genera a highy voatie one, with bit error rates potentiay varying over orders of magnitude even within a singe session as a user moves about or environmenta conditions change. Because of this, it is worthwhie and in fact extremey important to consider a system that is adaptive to environmenta conditions. This agorithm is suitabe for video and image transmission, because the quaity is not dependent on the environment or the distance between the base station (Access point) and the termina. Our agorithm therefore has an inherent characteristic that it maintains a constant received signa quaity. In addition to its ower power consumption, the proposed agorithm has the advantage of constant quaity suitabe for image transmission. The adaptive iteration agorithm is shown in Figure. Consider for exampe the case in which the present iteration states State. The TH < < TH shoud meet as: N TH represents the threshod for iteration state transits from State to State.Once the next data sot signa has been received, we cacuate the sot, as foows: of the received If If < then State State N N TH N N TH > then State State. In the traditiona agorithm, the threshod TH is a constant vaue and b TH N is equa to N TH +. In this paper, we integrate hysteresis into the constant N TH to reduce the transitions of the iteration state. Figure shows the Transfer Iteration State with hysteresis.

3 N TH N TH 3 N TH 4 3 N TH N N State Number of Iterations State Number of Iterations State 3 Number of Iterations 3 State 4 Number of Iterations 4 State N Number of Iterations N N TH N TH 3 N TH 3 4 N TH N-N Iteration State State + N State TH + N Fig. Adaptive Iteration gorithm. Fig. Transfer Iteration State from State to State. The received is as modeed as foows: x t) x + n ( () where n represents estimation error and is modeed as zero mean-independent with Gaussian process with variance σ. Figure 3 shows the BR performance for Turbo decoding in AWGN channe with no estimation error. The conditioned BR with different iteration numbers is shown in Tabe. Tabe shows the minimum N to achieve conditioned BR with fixed iteration number. For exampe, in condition BR 3, to achieve BR < 3, we decide the N. 85. If b / TH 3 4 b / N TH 3 4 >.85, then the number of iterations changes from 4 to 3. As above, N.3, N We assume A 4. 7, then / TH 3 / TH A4 + A.85 A b / TH 3 4 A3 + A.3 A. 69 b / TH 3 A + A A 4. (). b / TH The shown in simuation is assumed as: hysteresis ( A A ) (3) * +

4 BR Number of Iterations 3 Number of Iterations 4 Number of Iterations Number of Iterations (db) Fig. 3 Turbo decoding in AWGN channe, intereaver number76, coding rate /3. Tabe : Number of iterations in condition BR N ( db) Number of iterations BR N N N3 N Figures 4 shows that the adaptive iterations resut in condition BR 3 with different N estimation errors and hystereses. Based on the simuate resuts, we find that ower estimation error achieves better BR. The higher hysteresis wi achieve better BR performance. As the estimation error increases, the performance of BR degrades. In Figure 4(a), there are two BR notches, one between.9 to.4 and one between 3.4 to 3.9, because there are different iterations of the state transition threshod N. 3, N 3. 7 in these b / TH 3 b / TH respective areas. As estimation error increases, as shown in Figures 4(b), the BR curves become more fat than that shown in Figure 4(a). The notch phenomenon is not obvious, because the iteration stat is easy to transfer from one to the other with high measurement error hysteresis δ.6. hysteresis δ hysteresis δ.5.3 hysteresis δ.5. BR -4 BR hysteresis.5-6 hysteresis hysteresis hysteresis (db) (db) (a) N estimation error σ.6 (b) N estimation error σ.5 Fig. 4 Adaptive iterations resuts.

5 In order to evauate the number of transition under dynamic variation of caused by change of communication environment, we investigated the effect of hysteresis under AWGN channe. We assumed that the vaue changed ineary from A to A due to change in the communication environment; the change rate of the vaue was constant. The vaue x ( is modeed as foows: x + + k α + n (4), where k denotes a sampe number, α represents the change rate, and n represents the estimation error and is modeed as zero mean-independent with Gaussian process with variance σ. The term k α in the equation (4) means a variation in quantity of from A, measured at interva k. Let t ( denote the probabiity that there is a transition at interva k. denotes the probabiity of transition from A to A, and that of vice versa for the inverse transition is indicated by (. Then, if ( and ( denote the probabiity that the present iteration state is characterized by State and State respectivey, the foowing recursive reations hod: t( A ( k ) ( k )( ( k ) + A ) + + ( k ) A A ( k ) ( k )( ) (5), k,, A α, (), and ) as initia vaues. A( The agorithm considered performs a transition to the adjacent state if the foowing condition is met: the measured fas beow And ( can be evauated by + + or exceeds { x( < x( k > } + { State + ( State ( k )} + ) (6), { x( > x( k < } k State k State k (7). ( ) { ( ) ( )} ) +.

6 The foowing criteria may be used to assess the performance of the transition agorithm: ) Average number of transitions N t t (9) ) Average transition k N k / N (). b t t t k For numerica evauation, A, A, A 3, and A 4 are assumed to be 3.7,.3,.85, and.65 db, respectivey, on condition that BR 3. The incination α is assumed to be.. Figure 5 shows the probabiity of assignment to State and State and the probabiity of transition as the threshod eve is increased from to.3 db when the standard deviation of the N estimation error is σ.6 and.5db. From figure 5(a), in the case that estimation error is reativey sma, as the threshod eve increases, the intersections of the probabiities A ( and A shift away from the state boundary, resuting in a magnitude reduction as we as a right shift from the center in t (. When estimation error is reativey arge, transition probabiity t ( is even wider, and even if the threshod eve increases, the magnitude of the probabiity ony reduces and the probabiity doesn t shift much. Figure 6 shows the tradeoff curves between average number of transitions and average transition for increasing the threshod eve (.-.7 db) at the standard deviation of the N estimation error of σ.6 and.5 db. Increasing the threshod eve can reduce the average number of transitions. This figure aso shows how the estimate accuracy affects the performance of the agorithm. As the estimation error σ is increased, average number of transitions is extremey increased, that is, this means that the iteration state switches frequenty. robabiity A A.6.4. t / (db) robabiity A A.6.4 t / (db) (a) σ.6 (b) σ.5 Fig. 5 robabiity of assignment to State and State, and probabiity of transition.

7 Average number of transition Average transition / (db) Average number of transition Average transition / (db) (a) σ.6 (b) σ.5 Fig. 6 Average number of transitions versus average transition ; State through State. Figure 4 demonstrates the BR vs. under different estimation errors. Simuation resuts show some BR notches. If we want to have a fat BR curve, we need to seect an appicabe hysteresis. As shown in Figures 4, hysteresis.3 is suitabe to obtain a smooth BR curve. As shown in Figure 6, in the case of hysteresis.3, the average number of transitions is aso sufficienty sma. In Figure 4(b) it can be seen that when we increase the hysteresis for adaptive iterations in Turbo decoding, the performance of BR wi increase. The effects of increasing the hysteresis are the same in Figure 4(a). so, as shown in Figure 6, a arge hysteresis eve can remove unnecessary transitions. The performance in arge hysteresis wi be better than that in in sma hysteresis. However, in a arge hysteresis situation, the decoder has more opportunity to stay in a state of high iteration. The drawback of increased hysteresis is that the decoder utiizes more power in high average iterations; power consumption is proportiona to the number of iterations. Specificay, designers must consider a tradeoff between BR and power consumption. though we simuated our agorithm in the AWGN channe, this agorithm is aso suitabe for a sow fading environment. As resuts of the anaysis, ow noise environments give the cinica variation for the adaptive iteration agorithm. In our anaysis, ow noise environments provided sufficient cinica variation for the adaptive iteration agorithm and the hysteresis easiy controed the BR. This concusion is based on anaysis resuts of transition probabiity at a condition of noise σ.6. With regard to the resut of noise σ.6, shown in Figure 5 (a), the probabiity curve is critica. However, the curve of the adaptive iteration agorithm becomes broad when noise σ.5. This means that under this condition, hysteresis was not effective for the contro of BR performance; this resut was obtained by anaysis of transition probabiity when noise σ.5, as shown in Figure 5 (b). That is to say, when noise is sma, adaptive iteration is more effective. When noise is arge, BR performance is broad but hysteresis is not effective. This resut shows the infuence of the average number of transitions. When the noise is sma, the average number of transitions becomes once suddeny. When noise is arge, the average number of transitions cannot be reduced.

8 We studied the performance of an adaptive agorithm based on the measurement and the effect of the hysteresis in an AWGN environment in order to verify the feasibiity of the agorithm in practica appication. With this approach, the receiving stations determine for themseves the number of decoding iterations they need, based on the measurement. Moreover, this kind of adaptive iteration does not require signaing between sender and receiver. In this way, a considerabe amount of decoding power can be saved, and ow power consumption is essentia for portabe appications. As a consequence, the idea of adaptive decoding of turbo codes shows interesting potentia for future usage in indoor environments. The hysteresis wi affect the transition number of iterations, in that it infuences the average number of iterations and the performance of BR. A suitabe hysteresis must be seected in order to achieve good baance between power and performance. This research was fuy supported by Lite-on Technoogy, Taiwan. I woud ike to thank Mr. Robert Lai and Mr. Harrison Chen for providing encouragement and discussion support during the research. [] C. Berrrou, A. Gavieux, and. Thitimajshima, Near Shannon imit error-correcting coding and decoding: turbo-codes, ICC 993, Geneva, Switzerand, pp.64-7, May 993. [] S. Benedetto, D. Divsaar, G. Montorsi, and F. oara, A soft-input soft-output Maximum A osteriori (MA) modue to decode parae and seria concatenated codes, TDA progress report 4-7, November 5, 996. [3] 3G TS 5.: 3rd Generation artnership roject; Technica Specification Group Radio Access Network; Mutipexing and channe coding (FDD). [4] Harri Homa and Antti Toskaa, WCDMA for UMTS,. [5] Interim V&V Text for CDMA- hysica Layer (Revision 8.3), TIA, 999. [6] A. S. Barbuescu and S. S. ietrobon, Turbo codes: A tutoria on a new cass of powerfu error correcting coding schemes: art : Decoder design and performance, Journa of ectrica and ectronics ngineering, Austraia, vo. 9, pp. 43-5, Sept [7] John Dieissen, Jef van Meerbergen, and Marco Bekooij, ower efficient ayered turbo decoder processor impementation, accepted on, Munich. [8] F. Gibert et a., Low ower Impementation of a Turbo-Decoder on rogrammabe Architectures. AS-DAC,.