Weak Secrecy in the Multi-Way Untrusted Relay Channel with Compute-and-Forward

We investigate the problem of secure communications in a Gaussian multi-way relay channel applying the compute-and-forward scheme using nested lattice codes. All nodes employ half-duplex operation and can exchange confidential messages only via an untrusted relay. The relay is assumed to be honest but curious, i.e., an eavesdropper that conforms to the system rules and applies the intended relaying scheme. We start with the general case of the single-input multiple-output (SIMO) L-user multi-way relay channel and provide an achievable secrecy rate region under a weak secrecy criterion. We show that the securely achievable sum rate is equivalent to the difference between the computation rate and the multiple access channel (MAC) capacity. Particularly, we show that all nodes must encode their messages such that the common computation rate tuple falls outside the MAC capacity region of the relay. We provide results for the single-input single-output (SISO) and the multiple-input single-input (MISO) L-user multi-way relay channel as well as the two-way relay channel. We discuss these results and show the dependency between channel realization and achievable secrecy rate. We further compare our result to available results in the literature for different schemes and show that the proposed scheme operates close to the compute-and-forward rate without secrecy.Comment: submitted to JSAC Special Issue on Fundamental Approaches to Network Coding in Wireless Communication System

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

Slepian-Wolf Coding Over Cooperative Relay Networks

This paper deals with the problem of multicasting a set of discrete memoryless correlated sources (DMCS) over a cooperative relay network. Necessary conditions with cut-set interpretation are presented. A \emph{Joint source-Wyner-Ziv encoding/sliding window decoding} scheme is proposed, in which decoding at each receiver is done with respect to an ordered partition of other nodes. For each ordered partition a set of feasibility constraints is derived. Then, utilizing the sub-modular property of the entropy function and a novel geometrical approach, the results of different ordered partitions are consolidated, which lead to sufficient conditions for our problem. The proposed scheme achieves operational separation between source coding and channel coding. It is shown that sufficient conditions are indeed necessary conditions in two special cooperative networks, namely, Aref network and finite-field deterministic network. Also, in Gaussian cooperative networks, it is shown that reliable transmission of all DMCS whose Slepian-Wolf region intersects the cut-set bound region within a constant number of bits, is feasible. In particular, all results of the paper are specialized to obtain an achievable rate region for cooperative relay networks which includes relay networks and two-way relay networks.Comment: IEEE Transactions on Information Theory, accepte

An Information Theoretic Framework for Two-Way Relay Networks

We propose an information theoretic framework for scheduling the transmissions in a two-way multi-hop network. First we investigate some long standing open problems that were encountered during the course of the research. To illustrate their difficulty, we describe some failed attempts at resolving them. We then introduce the two-way one-relay channel. It turns out that the achievable rate region of this network has a nice interpretation, especially when viewed in the context of the open problems examined earlier. Motivated by this observation, we attempt to extend this achievable region to the two-way two-relay channel. In the process, we expose a fundamental deadlock problem in which each relay needs to decode before the other in order to enable mutual assistance. Our most important contribution is a resolution to this deadlock problem; we add an additional constraint that ensures some relay can decode at least one message before the other relay. Furthermore, we also introduce several coding schemes to prove that the additional constraint is indeed sufficient. Our schemes also show that information theory provides unique insight into scheduling the transmissions of multi-hop networks

Low-density Parity-check Codes for Wireless Relay Networks

In wireless networks, it has always been a challenge to satisfy high traffic throughput demands, due to limited spectrum resources. In past decades, various techniques, including cooperative communications, have been developed to achieve higher communication rates. This thesis addresses the challenges imposed by cooperative wireless networks, in particular focusing on practical code constructions and designs for wireless relay networks. The thesis is divided into the following four topics: 1) constructing and designing low-density parity-check (LDPC) codes for half-duplex three-phase two-way relay channels, 2) extending LDPC code constructions to half-duplex three-way relay channels, 3) proposing maximum-rate relay selection algorithms and LDPC code constructions for the broadcast problem in wireless relay networks, and 4) proposing an iterative hard interference cancellation decoder for LDPC codes in 2-user multiple-access channels. Under the first topic, we construct codes for half-duplex three-phase two-way relay channels where two terminal nodes exchange information with the help of a relay node. Constructing codes for such channels is challenging, especially when messages are encoded into multiple streams and a destination node receives signals from multiple nodes. We first prove an achievable rate region by random coding. Next, a systematic LDPC code is constructed at the relay node where relay bits are generated from two source codewords. At the terminal nodes, messages are decoded from signals of the source node and the relay node. To analyze the performance of the codes, discretized density evolution is derived. Based on the discretized density evolution, degree distributions are optimized by iterative linear programming in three steps. The optimized codes obtained are 26% longer than the theoretic ones. For the second topic, we extend LDPC code constructions from half-duplex three-phase two-way relay channels to half-duplex three-way relay channels. An achievable rate region of half-duplex three-way relay channels is first proved. Next, LDPC codes for each sub-region of the achievable rate region are constructed, where relay bits can be generated only from a received codeword or from both the source codeword and received codewords. Under the third topic, we study relay selection and code constructions for the broadcast problem in wireless relay networks. We start with the system model, followed by a theorem stating that a node can decode a message by jointly decoding multiple blocks of received signals. Next, the maximum rate is given when a message is decoded hop-by-hop or decoded by a set of nodes in a transmission phase. Furthermore, optimal relay selection algorithms are proposed for the two relay schemes. Finally, LDPC codes are constructed for the broadcast problem in wireless relay networks. For the fourth topic, an iterative hard interference cancellation decoder for LDPC codes in 2-user multiple-access channels is proposed. The decoder is based on log-likelihood ratios (LLRs). Interference is estimated, quantized and subtracted from channel outputs. To analyze the codes, density evolution is derived. We show that the required signal-to-noise ratio (SNR) for the proposed low-complexity decoder is 0.2 dB higher than that for an existing sub-optimal belief propagation decoder at code rate 1/3.4 month