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OFDM Modulated Cooperative Multiple-Access Channel With Network-Channel Coding

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TABLE OF CONTENTS Introduction OFDM System model of OFDM-CMAC Diversity order of outage probability Achievable Rates and Code Designs Code Design methodology Conclusion References 2

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INTRODUCTION consider the half-duplex cooperative multiple- access channel (CMAC) with frequency-selective block-fading. Each link employs an orthogonal frequency division multiplexing (OFDM) system, where modulated symbols are drawn from a finite constellation set. We first obtain the diversity order of the CMAC, as a function of the time sharing variables of the users and the rates of the code.

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To achieve this rate diversity tradeoff, we use the principle of network coding where messages of the two sources are jointly encoded Both separate and joint network-channel coding approaches are considered Specifically, we design multiple turbo codes that minimize the outage probabilities of these approaches. We also give a code structure for the multiple turbo codes to achieve full diversity of the system.

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OFDM Basic idea Frequency selective fading -In any radio transmission, the channel spectral response is not flat. It has fades in the response due to reflections causing cancellation of certain frequencies at the receiver. Reflections off near-by objects (e.g. ground, buildings, trees, etc) can lead to multipath signals of similar signal power as the direct signal. This can result in deep nulls in the received signal power due to destructive interference. For narrow bandwidth transmissions if the null in the frequency response occurs at the transmission frequency then the entire signal can be lost. This problem overcome by using OFDM trensmission. » Using a large number of parallel narrow-band subcarriers instead of a single wide-band carrier to transport information. Advantage: » Very easy and efficient in dealing with multi-path. » Robust again narrow-band interference

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System model of OFDM-CMAC In this paper, focus on the decode and-forward(DF) protocol under the framework of coded cooperation for cooperative multiple access channel (CMAC). We consider a time-division based half-duplex CMAC. With one antenna each, two sources S1 and S2 cooperate to deliver their messages to a common destination D.

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We assume a block-fading channel where the channel coefficients remain constant over the duration of one block consisting of channel uses, but are independently generated for each block. For each channel use, one modulated symbol is transmitted. For each link, we assume a frequency selective fading channel with multipaths, and an OFDM symbol that consists of subcarriers, where ≤. The normalized channel coefficients in the frequency domain for link (channel from node to node ) are denoted by g() = [() 1, ⋅ ⋅ ⋅, () ] where the subscript denotes the subcarrier index

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. Let ∣ () ∣ 2 = 1, where ∈ {1, 2} and ∈ {1, 2,}. We assume a reciprocal channel between S1 and S2, so g(12) = g(21). We denote the instantaneous SNR vector for link as () = ¯()g() ∘ (g()) ∗, where ∘ is the element wise multiplication, ¯() denotes the average SNR on link. The th element of () is the SNR for the th

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B. Achievable Rates and Code Designs Let (), or ()= the mutual information as a function of the instantaneous SNR, based on modulated symbols from the set of finite size 2. Assume that the corresponding () satisfies the following two properties. P1: (0) = 0 and () is a monotonically increasing function that approaches <∞. P2: (1) + (2) > (1 + 2), for sufficiently high 1 and 2

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consider the cooperation mode, where we assume 1 ≤ 1 12 and 2 ≤ 221. Each source therefore can decode the other message successfully and cooperate to transmit to D in the third time slot using STBC. By using independent codewords and joint decoding, an achievable rate region for (1,2) can be obtained as 1 ≤ 11 + 3STBC, (1) 2 ≤ 22 + 3STBC, (2) 1 + 2 ≤ 11 + 22 + 3STBC. Here, STBC =Σ =1 ((1) + (2) )/ is the mutual information achieved by the STBC coding

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DIVERSITY ORDER OF OUTAGE PROBABILITY The information theoretical limit for point-to-point block fading channels is the outage probability (0)out (¯,) =Pr( < ), where the random variable is the instantaneous mutual information of link =is the fixed transmission rate in bits per channel use. Assuming that the SNRs are independent for different links, the outage probability of CMAC can be written as out(¯,) = Pr( ℰ 12 ∪ ℰ 21)Pr( ℰ 1 ∪ ℰ 2)+Pr( ℰ 12 ∪ ℰ 21)Pr( ℰ COOP), where ℰ is the error event { > } that source fails to decode the message of source,

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CODE DESIGN METHODOLOGY We now develop the code design methodology for block fading channels. We first start with the diversity of the code, which affects the structure of the code. Once the structure is given, we look at how to optimize the coding gain of the code.

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CONCLUSION We have considered the problem of designing multiple turbo codes for the OFDM-CMAC in block- fading channels. We characterize the diversity order of the outage probability which depends in general on the time- sharing variables and the coding rates. In addition, we proposed a systematic code design method for OFDM-CMAC increase the reliability, link quality, and data rate of the system.

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[1] E. C. van der Meulen, “Three-terminal communication channels,” Advanced Applied Probability, vol. 3, pp. 120–154, 1971. [2] G. Kramer, M. Gastpar, and P. Gupta, “Cooperative strategies and capacity theorems for relay networks,” IEEE Trans. Inf. Theory, vol. 51, no. 9, pp. 3037– 3063, Sep. 2005. [3] A. Stefanov and E. Erkip, “Cooperative coding for wireless networks,”IEEE Trans. Commun., vol. 52, no. 9, pp. 1470–1476, Sep. 2004. [4] D. Duyck, J. J. Boutros, and M. Moeneclaey, “Low-densitygraph codes for slow fading relay channels.” Available:http://arxiv.org/abs/0903.1502, Mar. 09 [5] S. Katti, D. Katabi, W. Hu, H. Rahul, and M. Médard, “The importance of being opportunistic: practical network coding for wireless environments,” in Proc. 2005 Allerton Conf. on Comm., Control and Computing. [6] M. Effros, T. Ho, and S. Kim, “A tiling approach to network codingdesign,” in Proc. 2006 Information Theory Workshop. [7] L. Xiao, T. E. Fuja, J. Kliewer, and D. J. Costello, Jr., “A network coding approach to cooperative diversity,” IEEE Trans. Inf. Theory, vol. 53, no. 10, pp. 3714–3722, Oct. 2007. [8] C. Hausl and P. Dupraz, “Joint network-channel coding for the multipleaccess relay channel,” in Proc. 2006 International Workshop on WirelessAd-hoc and Sensor Networks pp. 817–822. REFERENCES

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