Accumulate Codes for Decode-and-Forward Wireless Relay Channel

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Linear Information Combining on RepeatAccumulate Codes for Decode-and-Forward Wireless Relay Channel Daryus Chandra and Sri Suning Kusumawardani  Abstract — Repeat-Accumulate Codes (RAC) are one of alternative choice code besides turbo codes and low-density parity-check (LDPC) codes. This paper presented decode-andforward protocol for wireless relay channel by utilizing repeataccumulate codes as the coding scheme in the relay. The main advantages of the RAC over another code that makes the RAC is more considered for this research are the complexity of encoding is linear in the code length, have a simpler design, and easier to combine with modulator or detector. Simplicity is the main factor for using RAC in this research because in the multihop wireless communication concept, the information processing that occurs in every node or in every relay should not be complicated. In this paper, RAC is employed in wireless relay channel and various post-decoding linear information combining methods are applied. The simulation results show that applying linear information combining after RAC decoding will improve the performance of wireless relay channel. For various position of the relay node, different linear information combining methods show the best performance. Keywords—Repeat-accumulate codes; RAC; cooperative communications; decode-and-forward; relay channel; information combining; linear combining

I. INTRODUCTION Wireless communication technology grows rapidly in recent years due to its ability to offer high mobility and high flexibility. However, many attempts to achieve reliable and high data-rate communication over the wireless channel have been unsuccessful due to multipath fading, shadowing, and path loss effects. One of several ideas to overcome those obstacles is cooperative communication. The basic idea of cooperative communication is described as follow: two or more mobile users are helping each other to forward information to the destination. In cooperative communication, the information source node (S) can act as relay node (R) and otherwise, the relay node (R) can act as the information source node (S) in order to reach the destination node (D). Cooperative communication scheme is considered capable on improving the reliability of wireless communication link. The key components that play important role on cooperative Manuscript received November 5, 2014. Daryus Chandra is with the Department of Electrical Engineering and Information Technology, Universitas Gadjah Mada, Indonesia. (e-mail: [email protected]). Sri Suning Kusumawardani is with the Department of Electrical Engineering and Information Technology, Universitas Gadjah Mada, Indonesia.

communications are the existence of the relays and the receiver diversity. Those, based on the basic principles and the idea of cooperatice communications, the relaying strategies or protocols, the information combining methods that performed by the receiver, and the coding scheme that employed in the systems are the important aspects to be developed further. The initial concept of cooperative communications is using relay only as a signal amplifier from the information source node (S) to the destination node (D) or vice versa [1],[2]. The concept of the simplest protocol is known as amplify-andforward (AF). Another well-known concept in cooperative communication is decode-and-forward (DF) [2],[3],[4]. The concept considers the relay has the regeneration function, meaning the received signal will be decoded before the forwarding stage, either uplink direction or downlink direction. The key concept for decode-and forward protocol is utilize powerful channel coding scheme in the relay. Another important component in DF concept is the receiver must perform information combining for both received information from the source and the relay. Some of the works already presented various applications of powerful channel coding schemes on relay channel such as RS-CC [5],[6], turbo codes [7],[8],[9], LDPC codes [10],[11], non-binary LDPC codes (NB-LDPC) [12],[13]. This paper presents decode-and-forward protocol by utilizing turbo-like coding which is better known as repeat-accumulate codes (RAC) [14]. Repeat-accumulate codes (RAC) have competitive performance compared to turbo codes and lowdensity parity check (LDPC) codes. The main advantage RA codes over another codes, such as LDPC codes and turbo codes, is RAC has lower complexity in both encoding and decoding process. Another property that makes RA codes more considerable in this research that is nonsystematic RA codes simpler to design when combined with modulator and detector [15]. Simple design is the fundamental factor for using RA codes in this research. In cooperative communications, the information processing that occurs in every node or in every relay should not be complicated. Previous research indicates that cooperative communications are able to reduce the average transmitted power per participating user even without exploiting any receive diversity benefit [16]. The purpose of this research is to investigate the performance of cooperative communications which exploit the receiver divesity benefit by performing information combining. The information combining on the

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receiver is performed by using linear diversity combining. There are three combining methods i.e. Selection Combining (SC), Equal Gain Combining (EGC), and Maximum Ratio Combining (MRC) [17]. The results will be compared to the system without information combining. This paper is organized as follows. Section II explains a brief introduction of repeat-accumulate codes. Section III explains the linear combining techniques that used in this research. Section IV introduces the system model which is applied throughout this research. Section V presents the simulation results of linear information combining which is combined with repeat-accumulate codes for wireless relay channel and finally section VI concludes the work. The main contribution of this research is to demonstrate the application of post-decoding linear information combining for wireless relay channel by utilizing repeat-accumulate codes as channel coding scheme. II. BRIEF EXPLANATION OF RAC RAC, as devised by Divsalar et al., consist of an outer code which is a repetition code and inner code which is an accumulator or a differential encoder or a unity rate convolutional code with single delay unit. The outer code and the inner code are separated by interleaver. Interleaver is used to avoid correlation between LLR which is exchanged between the outer code and inner code. The coding rate of RAC is defined by the coding rate of repetition code. In this paper, the each information bits is repeated twice, or in other words, the coding rate of RAC is ½. Construction of RAC encoder is shown in Figure 1.

Fig. 2 The decoder structure for RAC

III. LINEAR INFORMATION COMBINING Diversity techniques is developed to reduce the effects of fading channel. Diversity is achieved by separation of two or more radio channels by space, frequency, time, or even polarization. By applying diversity techniques, receiver has two or more copies of desired signals. By having two or more informations about the desired signal, receiver is able to utilize the informations for creating a better decision making. There are three wide-known linear diversity combining, there are Selection Combining (SC), Equal Gain Combining (EGC), and Maximum Ratio Combining (MRC). A. Selection Combining Selection combining is a switched technique, not a really combining method. The selection combining part simply picks out the best signal from N noisy received signal at a given time or period. This is a classical form of diversity techniques. In this paper the best signal is decided by measuring the signal to noise ratio (SNR) between the two channels in a given time period. The information from the channel with higher SNR value will be choosen for decision making of information bits. In mathematical form, SC method can be expressed in equation (1). (u )

L Fig. 1 The encoder structure of RAC

Decoding RAC is relatively simple compared to turbo codes, because only one decoder that performing log-MAP decoding [18]. The repeater decoder and the log-MAP decoder are serially-concatenated with one interleaver and one deinterleaver to perform iterative decoding, as shown in Figure 2. As it is a turbo-like decoding scheme, the log-MAP decoder is operated to obtain the extrinsic log-likelihood ratio (LLR). Input of log-MAP decoder is received input bits L(r) and a priori LLRs A(d). Those input values are required to calculate extrinsic LLRs E(d). To calculate extrinsic value and prediction bits L(u), the repetition decoder using a priori input A(v) which is a deinterleaved version of E(d). Before the a priori LLR E(v) is being the input of log-MAP decoder, E(v) is being interleaved to produce A(d), and it can be said that one iteration is complete.

(u )  Lsource if SNRSD  SNRRD   (u )   Lrelay if SNRSD  SNRRD

(1)

L(u) is the LLR value that used for deciding the predicted message bits from the information source, L(u)source is the LLR results from decoding process of received bits from the source node, and L(u)relay is the LLR results from decoding process of received bits from relay node. The value of signal to noise ratio (SNR) from each channel, source-destination (SD) channel and relay-destination (RD) channel, are defined by statistical measurement of received information from respective channel. B. Equal Gain Combining Equal gain combining is the simplest linear combining techniques that utilize all of the received informations. The equal gain combining part is performing addition to all channels with the same gain/proportion/ratio. Since all the information channels have the same proportion, it is not necessary for the infomation combiner to have knowledge about the corresponding channels condition. The equal gain combining decision making only relies on which decoder has more confindence regards to the decoded bits. The detailed

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2  SR  (1  d ) v 2  SD

(8)

work about the implementation of the implementation of EGC for information combining on wireless relay channels can be seen at [19]. In mathematical form, EGC method can be expressed as shown by equation (2). u) u) L(u )  L(source  L(relay

(2)

C. Maximum Ratio Combining Maximum ratio combining yields the maximum value of SNR from the received signals. The maximum output ratio is achieved if and only if the gain of each channel is proportional to the root mean square (RMS) of the received signal, or in other words, it is inversely proportional to the RMS of noise in the corresponding channel. In mathematical form, MRC method can be expressed as equation (3). u) u) L(u )  SNRRD  L(relay  SNRSD  L(source

(3)

The presented information combining techniques is performed after the decoding process of each received signal is already finished. Post-decoding combining is more considered in this paper because in the hardware implementation, synchronization is easier to be done when signals are in the digital form than the analog form. IV. SYSTEM MODEL In this paper, a system with one source node (S) and one relay node (R) is examined. The relay node (R) is placed on the direct link between the source node (S) and destination node (D), as showed in Figure 3. This model is widely used in research about wireless relay channel [11],[13],[20],[21].

The variable v is the attenuation or the path-loss exponent factor and d is the normalized distance between the information source and the relay. For example, the value of v is equal to 2 for line-of-sight (LOS) model and between 3 to 5 for urban channel model [22]. Based on the equation (7) and (8), the relationship of the signal-to-noise ratio (SNR) for each links are given by:

SNRSR  SNRSD.

1 dv

SNRRD  SNRSD.

1 (1  d )v

(9) (10)

From the equation (9) and (10), normalized transmit power by the source and the relay is one. Thus, the total normalized power used by a wireless communication system with relay is doubled from the power transmitted by the wireless communication system without a relay. In this paper, the model was modified so that the total normalized power transmitted by wireless communication with a relay system becomes equal to the normalized power transmitted by wireless communication systems without relay. Thus, equation (9) and (10) are modified, respectively, into equation (11) and (12) as follows:

1 1 SNRSR  .SNRSD. v 2 d 1 1 SNRRD  .SNRSD. 2 (1  d )v

(11) (12)

This model also appears in some works about wireless relay channels [23],[24]. The overall model for wireless relay channel which employs repeat-accumulate codes is depicted at Fig. 4. Fig. 3 A system with relay (R) on the direct link between the information source (S) and destination (D)

The distance between the source and the destination is normalized to 1 and 0 < d < 1 represents the distance between the source and the relay. By defining the noise terms as NSR, NRD, and NSD, respectively for S-R, R-D, and S-D links, the receive signal YSR, YRD, and YSD are given as follows: (4) Y  g H X N SR

SR

SR

S

SR

YSD  g SD H SDXS  N SD

(5)

YRD  g RD H RD X R  N RD

(6)

Assuming that S-R link, R-D link, and S-D link are AWGN 2 2 channels and noise powers are denoted as  SR ,  RD , and 2 , respectively, the relationship between the noise powers  SD of different links can be described as following equation:

2  SR  dv 2  SD

(7)

Fig. 4 The model of wireless communication system with relay using RA codes

In this paper, path-loss exponent factor v = 2 is used and different value of normalized distance d is considered, that are 1 1 3 d = ,1/2 d = , and d = . The detailed receiver model of 2 4 4 wireless communication with relay utilizing RA codes as the coding scheme for decode-and-forward is shown in Figure 5. Combining the information from the source and the relay is performed by linear diversity combining that is already presented. The resulting LLR which is used for making the decision about decoded bits is based on the information combining method.

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Fig. 5 Information combining performed by receiver at the destination

V. RESULTS AND DISCUSSION This part presents the simulation results of each method of linear diversity combining. The performance is measured by the bit error rate (BER) of decoded signals. The message frame-length is 2×104 bits or in other words the interleaver size is 4×104. The interleaver type that used to separate inner code and outer code is random interleaver. Figure 6 shows the performance of repeat-accumulate codes for wireless relay channel for various relay position and the receiver does not perform any information combining. It is clearly seen, for d = ½, even without exploiting any benefit from receiver diversity, cooperative communications schemes can provide better performance without increasing total power transmitted in the systems. In case d = ¼ and d = ¾. The wireless communication system with relays provide worse error correction performance results than the wireless communication system without relay. It is caused by the source which only transmits half of its normal power and become more suceptible to decoding errors on relay node. The decoding errors that occurs on relay node can propagate to destination node and can cause greater error decoding effects on destination.

Fig. 7 Performance of repeat-accumulate codes for wireless relay channel using selection combining

Fig. 8 Performance of repeat-accumulate codes for wireless relay channel using equal gain combining

Fig. 9 Performance of repeat-accumulate codes for wireless relay channel using maximum ratio combining Fig. 6 Performance of repeat-accumulate codes for wireless relay channel without information combining

Fig. 7, 8, and 9 shows the performance of of repeataccumulate codes for wireless relay channel for various relay position and the receiver perform linear information

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combining, respectively, Selection Combining (SC), Equal Gain Combining (EGC), and Maximum Ratio Combining (MRC). The results that depicted on Fig. 7, 8, and 9 shows that wireless communication using repeat-accumulate codes on wireless relay channel provide performance improvement compared to wireless communication system without relay. The worst performance occurs when relay is positioned d = ¾ of normalized distance between source and destination. This is caused by the source node only transmit half of its normal power but it has to propagate longer distance to reach the relay node. Since, the relay only provide single iteration, it is more suceptible to decoding errors and this error can propagate to destination node. Increasing the decoding iteration will overcome the problem but as the consequence it will increase delay processing at the relay.

Fig. 12 RAC performance for various information combining (relay position ¾ between information source to destination)

Fig. 10 RAC performance for various information combining (relay position ½ between information source to destination)

Fig. 10, 11, and 12, respectively show the simulation results for shows the performance of of repeat-accumulate codes for wireless relay channel for various linear information combining and the relay position, respectively, d = ½, d = ¼, and d = ¾. In general, it can be concluded that receiver which performing information combining will provide better performance compared to the system without information combining. It means that receiver will create a better decisionmaking if the receiver is provided more information from the source and the relay. In case deciding which information combining methods that will give the best performance, it is various for different relay position. For example for d = ½ and d = ¾, Selection Combining (SC) is superior compared to the others information combining, but in case d = ¼, Maximum Ratio Combing (MRC) shows the best performance. VI. CONCLUSION AND FUTURE WORKS

Fig. 11 RAC performance for various information combining (relay position ¼ between information source to destination)

In this paper, a system with, single user, single relay, path loss exponential factor v = 2, is considered. From the simulation results, it is clear that the wireless communication systems which using linear information combining have the superior performances compared with the systems without information combining. The linear information combining is successfully increase the performance of wireless communication system. For multihop system, it is not necessary to prove by simulation since it is already proven theoritically that increasing the relay/hop number will increase the performance of the wireless communication systems without increasing the total transmitted power of the systems even without performing information combining [16]. It is obvious that for multihop system using linear information combining will provide better performance. For higher value of path-loss exponent factor, it ia also unnecessary to be simulated since the previous works already shows that higher value of pathloss exponent factor will gain higher benefit from the

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cooperation [16],[19]. Some aspects that can be improved for future works is proving theoritically which linear information combining that will provide the optimal performance in general analytical form and finding the mechanism to combine all of linear information combining methods in hybrid modes. The improvement can also be focused on finding mechanism to prevent the decoding errors propagate to destination node. Some methods have been proposed to overcome this problem such as soft decode-and-forward [25],[26], partial decode-andforward [27], and partial soft decode-and-forward [28]. All of this improvement can be combined to provide the optimal performance of cooperative communications without increasing total transmitted power by the wireless communication systems.

[14]

[15]

[16]

[17] [18]

[19]

ACKNOWLEDGMENT The author would like to thank Telecommunication and High Frequency System Laboratory, Department of Electrical Engineering and Information Technology, Universitas Gadjah Mada for the support on this research.

[20]

[21]

REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

J. N. Laneman, G. W. Wornell, and D. N. C. Tse, “An Efficient Protocol for Realizing Cooperative Diversity in Wireless Networks,” in International Symposium on Information Theory, 2001, p. 294. J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative Diversity in Wireless Networks: Efficient Protocols and Outage Behavior,” IEEE Transactions on Information Theory, vol. 50, no. 12, pp. 3062–3080, Dec. 2004. A. Sendonaris, E. Erkip, and B. Aazhang, “User Cooperation Diversity - Part I: System Description,” IEEE Transactions on Communications, vol. 51, no. 11, pp. 1927–1938, 2003. A. Sendonaris, E. Erkip, and B. Aazhang, “User Cooperation Diversity - Part II : Implementation Aspects and Performance Analysis,” IEEE Transactions on Communications, vol. 51, no. 11, pp. 1939–1948, 2003. X. Liu, X. Sun, M. Jiang, and C. Zhao, “The Performance of RS-CC Concatenated Codes for the Relay Channel in WiMAX System,” in International Conference on Wireless Communications & Signal Processing, 2009, pp. 1–5. Y. M. H. Al-Moliki, K. A. Bin Noordin, M. N. Hindia, and M. F. B. M. Salleh, “Concatenated RS-Convolutional Communication Codes for Cooperative Wireless,” Open Electrical & Electronic Engineering Journal, vol. 7, pp. 9–20, 2013. B. Zhao and M. C. Valenti, “Cooperative Diversity using Distributed Turbo Codes,” in Proceeding of Virginia Tech Symposium on Wireless Personal Commununication, 2003, pp. 1–10. B. Zhao and M. C. Valenti, “Distributed Turbo Coded Diversity for Relay Channel,” Electronics Letter, vol. 39, no. 10, pp. 786–787, 2003. M. C. Valenti and B. Zhao, “Distributed Turbo Codes: Towards the Capacity of the Relay Channel,” in IEEE 58th Vehicular Technology Conference, 2003, pp. 322–326. K. J. Kim, P. Wang, D. Kwak, and K. S. Kwak, “Distributed LDPC Coders in Cooperative Relay Networks,” in International Symposium on Communications and Information Technology, 2009, pp. 949–953. M. Wu, P. Weitkemper, W. Dirk, and K.-D. Kammeyer, “Comparison of Distributed LDPC Coding Schemes for Decode-and-Forward Relay Channels,” in International ITG Workshop on Smart Antennas, 2010, pp. 127–134. P. Suthisopapan, K. Kasai, A. Meesomboon, V. Imtawil, and K. Sakaniwa, “Simple Low-Rate Non-Binary LDPC Coding for Relay Channels,” 2011, pp. 1–9. P. Suthisopapan, K. Kasai, A. Meesomboon, V. Imtawil, and K. Sakaniwa, “Simple Nonbinary Coding Strategy for Very Noisy Relay,”

[22] [23]

[24]

[25]

[26]

[27]

[28]

CHANDRA & KUSUMAWARDANI

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. 95, no. 12, pp. 1–8, 2012. D. Divsalar, H. Jin, and R. J. McEliece, “Coding Theorems for ‘TurboLike’ Codes,” in Annual Allerton Conference on Communication, Control, and Computing, 1998, pp. 201–210. S. Brink and G. Kramer, “Design of Repeat-Accumulate Codes for Iterative Detection and Decoding,” IEEE Transactions on Signal Processing, vol. 51, no. 11, pp. 2764–2772, 2003. D. S. Michalopoulos and R. Schober, “Can Cooperation Reduce The Average Transmitted Power per Participating User?,” in IEEE Global Communications Conference (GLOBECOM), 2013, pp. 3884–3889. D. G. Brennan, “Linear Diversity Combining Techniques,” Proceedings of the IEEE, vol. 91, no. 2, pp. 331–356, 2003. S. Shamsy, “EXIT Chart Analysis of Repeat Accumulate Codes for Log-BCJR Algorithm in Iterative Decoding,” in 1st International Conference on Communications, Signal Processing, and their Applications (ICCSPA), 2013, pp. 1–5. D. Chandra, A. Susanto, and S. S. Kusumawardani, “Performance of Repeat-Accumulate Codes (RAC) for Decode-and-Forward Wireless Relay Channel,” in International Conference on Electrical Engineering and Information Technology (ICITEE), 2014, pp. 214– 219. Y. Li, B. Vucetic, T. F. Wong, and M. Dohler, “Distributed Turbo Coding With Soft Information Relaying in Multihop Relay Networks,” IEEE Journal on Selected Areas in Communications, vol. 24, no. 11, pp. 2040–2050, 2006. M. Benjillali and L. Szczecinski, “A Simple Detect-and-Forward Scheme in Fading Channels,” IEEE Communications Letters, vol. 13, no. 5, pp. 309–311, May 2009. T. S. Rappaport, Wireless Communications: Principles and Practices, 2nd ed. New Jersey: Prentice-Hall, 2002. A. Florea and H. Yanikomeroglu, “On the Optimal Number of Hops in Infrastructure-Based Fixed Relay Networks,” IEEE Global Telecommunications Conference (GLOBECOM), pp. 3242–3247, 2005. S. Kim and W. E. Stark, “On the Optimal Number of Hops in Relay Networks,” in IEEE International Conference on Communications (ICC), 2012, pp. 5080–5085. H. H. Sneessens and L. Vandendorpe, “Soft Decode and Forward Improves Cooperative Communications,” in IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2005, pp. 157–160. P. Huo and L. Cao, “Soft Decode-and-Forward Cooperative Communication with Distributed Space-Time Coding,” AEU International Journal of Electronics and Communications, vol. 67, no. 10, pp. 861–867, Oct. 2013. J. Y. Ryu, W. Choi, and D. I. Kim, “A Novel Partial Decode-andForward Relaying with Multiple Antennas,” in IEEE 72nd Vehicular Technology Conference - Fall, 2010, pp. 1–5. P. S. Ahmed, R. G. Maunder, and L. Hanzo, “Partial Soft Decode and Forward,” in IEEE Vehicular Technology Conference, 2011, pp. 1–5.

Daryus Chandra received his bachelor degree (S.T.) in electrical engineering specialized in telecommunication engineering and master degree (M.Eng.) in electrical engineering specialized in electronics signal systems from Department of Electrical Engineering and Information Technology, Universitas Gadjah Mada, Indonesia, respectively in 2013 and 2014. His research interest are channel coding and wireless communications. Sri Suning Kusumawardani received her bachelor degree (S.T.), master degree (M.T.), and doctorate degree (Dr.) in electrical engineering from Department of Electrical Engineering and Information Technology, Universitas Gadjah Mada, Indonesia, respectively in 1995, 2001, and 2015. She was attending Sandwich Program in Engineering Education, Utah State University, USA in 2009 and Erasmus Mundus Research Program, Universitat Politècnica de Catalunya, Spain in 2013. Currently, she is an Associate Professor in Department of Electrical Engineering and Information Technology, Universitas Gadjah Mada, Indonesia. Her research interest including simulation and implementation of channel coding and computer networks.

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