A Unified Relay Framework with both D-F and C-F Relay Nodes

Decode-and-forward (D-F) and compress-and-forward (C-F) are two fundamentally different relay strategies proposed by (Cover and El Gamal, 1979). Individually, either of them has been successfully generalized to multi-relay channels. In this paper, to allow each relay node the freedom of choosing either of the two strategies, we propose a unified framework, where both the D-F and C-F strategies can be employed simultaneously in the network. It turns out that, to fully incorporate the advantages of both the best known D-F and C-F strategies into a unified framework, the major challenge arises as follows: For the D-F relay nodes to fully utilize the help of the C-F relay nodes, decoding at the D-F relay nodes should not be conducted until all the blocks have been finished; However, in the multi-level D-F strategy, the upstream nodes have to decode prior to the downstream nodes in order to help, which makes simultaneous decoding at all the D-F relay nodes after all the blocks have been finished inapplicable. To tackle this problem, nested blocks combined with backward decoding are used in our framework, so that the D-F relay nodes at different levels can perform backward decoding at different frequencies. As such, the upstream D-F relay nodes can decode before the downstream D-F relay nodes, and the use of backward decoding at each D-F relay node ensures the full exploitation of the help of both the other D-F relay nodes and the C-F relay nodes. The achievable rates under our unified relay framework are found to combine both the best known D-F and C-F achievable rates and include them as special cases

Coding Schemes for Multiple-Relay Channels

In network information theory, the relay channel models a communication scenario where there is one or more relay nodes that can help the information transmission between the source and the destination. Although the capacity of the relay channel is still unknown even in the single-relay case, two fundamentally different relay schemes have been developed by (Cover and El Gamal, 1979) for such channels, which, depending on whether the relay decodes the information or not, are generally known as Decode-and-Forward (D-F) and Compress-and-Forward (C-F). In the D-F relay scheme, the relay first decodes the message sent by the source and then forwards it to the destination, and the destination decodes the message taking into account the inputs of both the source and the relay. In contrast, the C-F relay scheme is used when the relay cannot decode the message sent by the source, but still can help by compressing its observation into some compressed version, and forwarding this compression into the destination; the destination then either successively or jointly decodes the compression of the relay's observation and the original message of the source. For the single-relay case, it is known that joint compression-message decoding, although providing more freedom in choosing the compression at the relay, cannot achieve higher rates for the original message than successive decoding. This thesis addresses some fundamental issues in generalizing and unifying the above D-F and C-F relay schemes to the multiple-relay case. We first generalize the C-F scheme to multiple-relay channels, and investigate the question of whether compression-message joint decoding can improve the achievable rate compared to successive decoding in the multiple-relay case. It is demonstrated that in the case of multiple relays, there is no improvement on the achievable rate by joint decoding either. More interestingly, it is discovered that any compressions not supporting successive decoding will actually lead to strictly lower achievable rates for the original message. Therefore, to maximize the achievable rate for the original message, the compressions should always be chosen to support successive decoding. Furthermore, it is shown that any compressions not completely decodable even with joint decoding will not provide any contribution to the decoding of the original message. We also develop a new C-F relay scheme with block-by-block backward decoding. This new scheme improves the original C-F relay scheme to achieve higher rates in the multiple-relay case as the recently proposed noisy network coding scheme. However, compared to noisy network coding which uses repetitive encoding/all blocks united decoding, our new coding scheme is not only simpler, but also reveals the essential reason for the improvement of the achievable rate, that is, delayed decoding until all the blocks have been finished. Finally, to allow each relay node the freedom of choosing either the D-F or C-F relay strategy, we propose a unified relay framework, where both the D-F and C-F strategies can be employed simultaneously in the network. This framework employs nested blocks combined with backward decoding to allow for the full incorporation of the best known D-F and C-F relay strategies. The achievable rates under our unified relay framework are found to combine both the best known D-F and C-F achievable rates and include them as special cases. It is also demonstrated through a Gaussian network example that our achievable rates are generally better than the rates obtained with existing unified schemes and with D-F or C-F alone

How to Understand LMMSE Transceiver Design for MIMO Systems From Quadratic Matrix Programming

In this paper, a unified linear minimum mean-square-error (LMMSE) transceiver design framework is investigated, which is suitable for a wide range of wireless systems. The unified design is based on an elegant and powerful mathematical programming technology termed as quadratic matrix programming (QMP). Based on QMP it can be observed that for different wireless systems, there are certain common characteristics which can be exploited to design LMMSE transceivers e.g., the quadratic forms. It is also discovered that evolving from a point-to-point MIMO system to various advanced wireless systems such as multi-cell coordinated systems, multi-user MIMO systems, MIMO cognitive radio systems, amplify-and-forward MIMO relaying systems and so on, the quadratic nature is always kept and the LMMSE transceiver designs can always be carried out via iteratively solving a number of QMP problems. A comprehensive framework on how to solve QMP problems is also given. The work presented in this paper is likely to be the first shoot for the transceiver design for the future ever-changing wireless systems.Comment: 31 pages, 4 figures, Accepted by IET Communication

A Unified Approach for Network Information Theory

In this paper, we take a unified approach for network information theory and prove a coding theorem, which can recover most of the achievability results in network information theory that are based on random coding. The final single-letter expression has a very simple form, which was made possible by many novel elements such as a unified framework that represents various network problems in a simple and unified way, a unified coding strategy that consists of a few basic ingredients but can emulate many known coding techniques if needed, and new proof techniques beyond the use of standard covering and packing lemmas. For example, in our framework, sources, channels, states and side information are treated in a unified way and various constraints such as cost and distortion constraints are unified as a single joint-typicality constraint. Our theorem can be useful in proving many new achievability results easily and in some cases gives simpler rate expressions than those obtained using conventional approaches. Furthermore, our unified coding can strictly outperform existing schemes. For example, we obtain a generalized decode-compress-amplify-and-forward bound as a simple corollary of our main theorem and show it strictly outperforms previously known coding schemes. Using our unified framework, we formally define and characterize three types of network duality based on channel input-output reversal and network flow reversal combined with packing-covering duality.Comment: 52 pages, 7 figures, submitted to IEEE Transactions on Information theory, a shorter version will appear in Proc. IEEE ISIT 201

Diversity, Coding, and Multiplexing Trade-Off of Network-Coded Cooperative Wireless Networks

In this paper, we study the performance of network-coded cooperative diversity systems with practical communication constraints. More specifically, we investigate the interplay between diversity, coding, and multiplexing gain when the relay nodes do not act as dedicated repeaters, which only forward data packets transmitted by the sources, but they attempt to pursue their own interest by forwarding packets which contain a network-coded version of received and their own data. We provide a very accurate analysis of the Average Bit Error Probability (ABEP) for two network topologies with three and four nodes, when practical communication constraints, i.e., erroneous decoding at the relays and fading over all the wireless links, are taken into account. Furthermore, diversity and coding gain are studied, and advantages and disadvantages of cooperation and binary Network Coding (NC) are highlighted. Our results show that the throughput increase introduced by NC is offset by a loss of diversity and coding gain. It is shown that there is neither a coding nor a diversity gain for the source node when the relays forward a network-coded version of received and their own data. Compared to other results available in the literature, the conclusion is that binary NC seems to be more useful when the relay nodes act only on behalf of the source nodes, and do not mix their own packets to the received ones. Analytical derivation and findings are substantiated through extensive Monte Carlo simulations.Comment: IEEE International Conference on Communications (ICC), 2012. Accepted for publication and oral presentatio

Cooperative Lattice Coding and Decoding

A novel lattice coding framework is proposed for outage-limited cooperative channels. This framework provides practical implementations for the optimal cooperation protocols proposed by Azarian et al. In particular, for the relay channel we implement a variant of the dynamic decode and forward protocol, which uses orthogonal constellations to reduce the channel seen by the destination to a single-input single-output time-selective one, while inheriting the same diversity-multiplexing tradeoff. This simplification allows for building the receiver using traditional belief propagation or tree search architectures. Our framework also generalizes the coding scheme of Yang and Belfiore in the context of amplify and forward cooperation. For the cooperative multiple access channel, a tree coding approach, matched to the optimal linear cooperation protocol of Azarain et al, is developed. For this scenario, the MMSE-DFE Fano decoder is shown to enjoy an excellent tradeoff between performance and complexity. Finally, the utility of the proposed schemes is established via a comprehensive simulation study.Comment: 25 pages, 8 figure