Multilevel Coding Schemes for Compute-and-Forward with Flexible Decoding

We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute and forward paradigm, we present a multilevel coding scheme that permits computation (or, decoding) of a class of functions at the relay. The function to be computed (or, decoded) is then chosen depending on the channel realization. We define such a class of functions which can be decoded at the relay using the proposed coding scheme and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using the QPSK constellation. Numerical results with QPSK show that the flexibility afforded by our proposed scheme results in substantially higher rates than those achievable by always using a fixed function or by adapting the function at the relay but coding over GF(4).Comment: This paper was submitted to IEEE Transactions on Information Theory in July 2011. A shorter version also appeared in the proceedings of the International Symposium on Information Theory in August 2011 without the proof of the main theore

Amplify-and-Forward in Wireless Relay Networks

A general class of wireless relay networks with a single source-destination pair is considered. Intermediate nodes in the network employ an amplify-and-forward scheme to relay their input signals. In this case the overall input-output channel from the source via the relays to the destination effectively behaves as an intersymbol interference channel with colored noise. Unlike previous work we formulate the problem of the maximum achievable rate in this setting as an optimization problem with no assumption on the network size, topology, and received signal-to-noise ratio. Previous work considered only scenarios wherein relays use all their power to amplify their received signals. We demonstrate that this may not always maximize the maximal achievable rate in amplify-and-forward relay networks. The proposed formulation allows us to not only recover known results on the performance of the amplify-and-forward schemes for some simple relay networks but also characterize the performance of more complex amplify-and-forward relay networks which cannot be addressed in a straightforward manner using existing approaches. Using cut-set arguments, we derive simple upper bounds on the capacity of general wireless relay networks. Through various examples, we show that a large class of amplify-and-forward relay networks can achieve rates within a constant factor of these upper bounds asymptotically in network parameters.Comment: Minor revision: fixed a typo in eqn. reference, changed the formatting. 30 pages, 8 figure

Achievable Rate Regions of Two-Way Relay Channels

With the fast development of communication networks, cooperative communication has been more widely used in many different fields, such as satellite networks, broadcast networks, internet and so on. Therefore relay channels have been playing a pivotal role since their definitions were proposed by Van-der Meulen. However, the general achievable rate region of a relay channel is still unknown which inspires more people to persistently work on. There are several different kinds of coding schemes proposed by people after relay channels came into our lives. Until now, the two most commonly used coding strategies of relay channels are Decode-and-Forward and Compress-and-Forward. In this thesis we will provide a way to obtain the achievable rate region for two-way relay channels by using decode-and-forward coding. With the knowledge of basic information theory and network information theory, we will focus our study on the achievable rates of relay channels. Most of the previous study of relay channels are aiming to find a more general achievable rate region. In this thesis, an intuitional way will be used to study four-terminal relay channels. This method makes a good use of the information from three-terminal relay channels by separating a four-terminal relay channel into two parts: (1). a three-terminal relay channel; (2). a common end node. The final achievable rate region is obtained by combing together the separate achievable rates of the two parts. We split the complex model to two easier ones, this idea may give help for doing researches on more complicated channels. Eliminating interferences is also a difficulty in the study of relay channels. Comparing with the achievable rate regions of two-way two-relay channels which have already been proved, we found that it is feasible to separate a two-way two-relay channel into a three-terminal relay channel and an common end node. Therefore, we apply this method to all two-way four-terminal relay channels. After fixing two different source nodes, all of the possible transmission schemes are presented in this thesis. However not all of the four-terminal channels can be separated into two parts. By studying the schemes failed to be decomposed to a three-terminal relay channel and a common end node, we found that these schemes are infeasible for message transmission. Thus our method can still be used to study on feasible two-way relay channels