Lossy Source Transmission over the Relay Channel

📝 Abstract

Lossy transmission over a relay channel in which the relay has access to correlated side information is considered. First, a joint source-channel decode-and-forward scheme is proposed for general discrete memoryless sources and channels. Then the Gaussian relay channel where the source and the side information are jointly Gaussian is analyzed. For this Gaussian model, several new source-channel cooperation schemes are introduced and analyzed in terms of the squared-error distortion at the destination. A comparison of the proposed upper bounds with the cut-set lower bound is given, and it is seen that joint source-channel cooperation improves the reconstruction quality significantly. Moreover, the performance of the joint code is close to the lower bound on distortion for a wide range of source and channel parameters.

💡 Analysis

Lossy transmission over a relay channel in which the relay has access to correlated side information is considered. First, a joint source-channel decode-and-forward scheme is proposed for general discrete memoryless sources and channels. Then the Gaussian relay channel where the source and the side information are jointly Gaussian is analyzed. For this Gaussian model, several new source-channel cooperation schemes are introduced and analyzed in terms of the squared-error distortion at the destination. A comparison of the proposed upper bounds with the cut-set lower bound is given, and it is seen that joint source-channel cooperation improves the reconstruction quality significantly. Moreover, the performance of the joint code is close to the lower bound on distortion for a wide range of source and channel parameters.

📄 Content

arXiv:0805.2996v1 [cs.IT] 20 May 2008 Lossy Source Transmission over the Relay Channel Deniz G¨und¨uz ∗†, Elza Erkip ‡∗, Andrea J. Goldsmith †, H. Vincent Poor ∗ ∗Dept. of Electrical Engineering, Princeton University, Princeton, NJ, 08544 †Dept. of Electrical Engineering, Stanford University, Stanford, CA 94305 ‡Dept. of Electrical and Computer Engineering, Polytechnic University, Brooklyn, NY 11201 Email: dgunduz@princeton.edu,elza@poly.edu,andrea@wsl.stanford.edu,poor@princeton.edu Abstract— Lossy transmission over a relay channel in which the relay has access to correlated side information is consid- ered. First, a joint source-channel decode-and-forward scheme is proposed for general discrete memoryless sources and channels. Then the Gaussian relay channel where the source and the side information are jointly Gaussian is analyzed. For this Gaussian model, several new source-channel cooperation schemes are introduced and analyzed in terms of the squared-error distortion at the destination. A comparison of the proposed upper bounds with the cut-set lower bound is given, and it is seen that joint source-channel cooperation improves the reconstruction quality significantly. Moreover, the performance of the joint code is close to the lower bound on distortion for a wide range of source and channel parameters. I. INTRODUCTION In many sensor network applications, the goal is to obtain a high fidelity reconstruction of an underlying physical phe- nomenon at the access point. While sensors might each try to send their own observations directly to the access point, this might result in poor reconstruction quality due to the power limitations of the sensor nodes. Cooperative transmission, in which the nearby nodes help each other’s transmissions, has been analyzed extensively in the literature as a promising technique to overcome the power limitation [1], [2]. However, in many sensor network applications, the sensor observations are highly correlated. It is natural to exploit correlated source coding together with cooperative communication, and this might lead to better reconstruction at the access point than using these two techniques independently. Finding the optimal strategy in terms of the end-to-end reconstruction fidelity in a general network is a very difficult problem. In fact, we do not even know the necessary and sufficient conditions for lossless transmission over simple network components such as multiple access or broadcast channels with correlated sources [3], [4]. There are some special cases for which the optimal performance has been characterized [5]-[7]. However, it is likely that the optimal performance requires joint source- channel coding (e.g. [7], [8]), as Shannon’s source-channel separation theorem does not apply to multi-terminal scenarios in general. This research was supported in part by the U.S. National Science Foun- dation under Grants ANI-03-38807, CCF-04-30885, CCF-06-35177, CCF-07- 28208, and CNS-06-25637 and the DARPA’s ITMANET program under Grant 1105741-1-TFIND, and the ARO under MURI award W911NF-05-1-0246. In this paper, we consider cooperative transmission in which the relay has correlated side information. The goal is to recon- struct the observation of the source terminal at the destination with the least possible distortion. In this scenario, the relay terminal can help the source by both improving the channel transmission rates and by reducing the source compression distortion. In general, the problem is a joint source-channel coding problem, and characterization of the necessary and sufficient conditions is an open problem. We considered this problem for lossless transmission in [6] and gave the necessary and sufficient conditions for some special cases. In [9], we focused on the Gaussian relay channel with quadratic Gaussian sources, and provided achievable schemes and comparisons with the joint source-channel cut-set bound. The proposed joint source-channel relaying schemes in [9] are grouped into three types. In the first group, called channel cooperation, the relay simply ignores its side information, and applies one of the well-known cooperative transmission schemes such as decode- and-forward (DF) or compress-and-forward (CF) [1]. In the second group, called source cooperation, the relay ignores its received signal and uses only its side information either by uncoded transmission followed by MMSE estimation at the decoder, or by a separation-based scheme in which the source and the relay first compress their sources at rates specified by one-helper source coding problem [11] and then transmit the compressed information separately by multiple access channel coding [9]. Finally, in the third group, called hybrid cooperation, the relay sends a superposition of channel and source cooperation codewords by a suitable power allocation. It is shown in [9] that hybrid cooperation performs better than either of the other two types, and approaches the cut-set lower bound closely for

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