Asymptotic Analysis on Spatial Coupling Coding for Two-Way Relay Channels

Compute-and-forward relaying is effective to increase bandwidth efficiency of wireless two-way relay channels. In a compute-and-forward scheme, a relay tries to decode a linear combination composed of transmitted messages from other terminals or relays. Design for error correcting codes and its decoding algorithms suitable for compute-and-forward relaying schemes are still important issue to be studied. In this paper, we will present an asymptotic performance analysis on LDPC codes over two-way relay channels based on density evolution (DE). Because of the asymmetric nature of the channel, we employ the population dynamics DE combined with DE formulas for asymmetric channels to obtain BP thresholds. In addition, we also evaluate the asymptotic performance of spatially coupled LDPC codes for two-way relay channels. The results indicate that the spatial coupling codes yield improvements in the BP threshold compared with corresponding uncoupled codes for two-way relay channels.Comment: 5 page

Joint Compute and Forward for the Two Way Relay Channel with Spatially Coupled LDPC Codes

We consider the design and analysis of coding schemes for the binary input two way relay channel with erasure noise. We are particularly interested in reliable physical layer network coding in which the relay performs perfect error correction prior to forwarding messages. The best known achievable rates for this problem can be achieved through either decode and forward or compute and forward relaying. We consider a decoding paradigm called joint compute and forward which we numerically show can achieve the best of these rates with a single encoder and decoder. This is accomplished by deriving the exact performance of a message passing decoder based on joint compute and forward for spatially coupled LDPC ensembles.Comment: This paper was submitted to IEEE Global Communications Conference 201

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

Code Design for Multihop Wireless Relay Networks

We consider a wireless relay network, where a transmitter node communicates with a receiver node with the help of relay nodes. Most coding strategies considered so far assume that the relay nodes are used for one hop. We address the problem of code design when relay nodes may be used for more than one hop. We consider as a protocol a more elaborated version of amplify-and-forward, called distributed space-time coding, where the relay nodes multiply their received signal with a unitary matrix, in such a way that the receiver senses a space-time code. We first show that in this scenario, as expected, the so-called full-diversity condition holds, namely, the codebook of distributed space-time codewords has to be designed such that the difference of any two distinct codewords is full rank. We then compute the diversity of the channel, and show that it is given by the minimum number of relay nodes among the hops. We finally give a systematic way of building fully diverse codebooks and provide simulation results for their performance

Wireless network coding for multi-hop relay channels

Future wireless communication systems are required to meet growing demands for high spectral e�ciency, low energy consumption and high mobility. The advent of wireless network coding (WNC) has o�ered a new opportunity to improve network throughput and transmission reliability by exploiting interference in intermediate relays. Combined with network coding and self-information cancelation, WNC for two-way relay channels (TWRCs) has come to the forefront. This dissertation focuses on exploiting WNC in multi-hop two-way relay channels (MH-TRCs). Particularly, a multi-hop wireless network coding (MH-WNC) scheme is designed for the generalized L-node K-message MH-TRC. Theoretical studies on the network throughput and performance bounds achieved by the MH-WNC scheme with di�erent relaying strategies (i.e., amplify-and-forward (AF) and compute-and-forward (CPF)) are carried out. Furthermore, by introducing di�erent numbers of transmission time intervals into the MH-WNC, a multiple-time-interval (Multi-TI) MH-WNC is proposed to determine an optimal MH-WNC which can achieve the best outage performance for all-scale MH-TRCs. Finally, this study extends the research on WNC one step forward from two-user networks to multi-user networks. An extended CPF joint with a dominated solution for maximizing the overall computation rate is proposed for the multi-way relay channel (mRC) in the last chapter. The contributions of this dissertation are multifold. First, the proposed MHWNC scheme with fixed two transmission time intervals can achieve a significantly improved network throughput compared to the non-network coding (Non-NC) scheme in the generalized L-node K-message MH-TRC. Theoretical results are derived for both multi-hop analog network coding (MH-ANC) and multi-hop compute-and-forward (MH-CPF). Moreover, both theoretical and numerical results demonstrate that the two MH-WNC schemes can be applied to different scale MH-TRCs to achieve a better outage performance compared to the conventional Non-NC scheme (i.e., MH-ANC for the non-regenerative MH-TRC with a small number of nodes, and MH-CPF for the regenerative MH-TRC with a large number of nodes.). Furthermore, a Multi-TI MH-WNC scheme is generalized with a special binary-tree model and characteristic matrix. The determined optimal MH-WNC scheme is able to provide the best outage performance and outperform the Non-NC scheme in all scale MH-TRCs. Last but not least, this dissertation provides a preliminary investigation of WNC in mRCs. The proposed dominated solution for maximizing the overall computation rate can ensure that all the nodes in the mRC successfully recover their required messages. Moreover, the extended CPF strategy is proven superior to Non-NC in the mRC with a small number of users