Diversity analysis, code design, and tight error rate lower bound for binary joint network-channel coding

Joint network-channel codes (JNCC) can improve the performance of communication in wireless networks, by combining, at the physical layer, the channel codes and the network code as an overall error-correcting code. JNCC is increasingly proposed as an alternative to a standard layered construction, such as the OSI-model. The main performance metrics for JNCCs are scalability to larger networks and error rate. The diversity order is one of the most important parameters determining the error rate. The literature on JNCC is growing, but a rigorous diversity analysis is lacking, mainly because of the many degrees of freedom in wireless networks, which makes it very hard to prove general statements on the diversity order. In this article, we consider a network with slowly varying fading point-to-point links, where all sources also act as relay and additional non-source relays may be present. We propose a general structure for JNCCs to be applied in such network. In the relay phase, each relay transmits a linear transform of a set of source codewords. Our main contributions are the proposition of an upper and lower bound on the diversity order, a scalable code design and a new lower bound on the word error rate to assess the performance of the network code. The lower bound on the diversity order is only valid for JNCCs where the relays transform only two source codewords. We then validate this analysis with an example which compares the JNCC performance to that of a standard layered construction. Our numerical results suggest that as networks grow, it is difficult to perform significantly better than a standard layered construction, both on a fundamental level, expressed by the outage probability, as on a practical level, expressed by the word error rate

Wireless Network Information Flow: A Deterministic Approach

In a wireless network with a single source and a single destination and an arbitrary number of relay nodes, what is the maximum rate of information flow achievable? We make progress on this long standing problem through a two-step approach. First we propose a deterministic channel model which captures the key wireless properties of signal strength, broadcast and superposition. We obtain an exact characterization of the capacity of a network with nodes connected by such deterministic channels. This result is a natural generalization of the celebrated max-flow min-cut theorem for wired networks. Second, we use the insights obtained from the deterministic analysis to design a new quantize-map-and-forward scheme for Gaussian networks. In this scheme, each relay quantizes the received signal at the noise level and maps it to a random Gaussian codeword for forwarding, and the final destination decodes the source's message based on the received signal. We show that, in contrast to existing schemes, this scheme can achieve the cut-set upper bound to within a gap which is independent of the channel parameters. In the case of the relay channel with a single relay as well as the two-relay Gaussian diamond network, the gap is 1 bit/s/Hz. Moreover, the scheme is universal in the sense that the relays need no knowledge of the values of the channel parameters to (approximately) achieve the rate supportable by the network. We also present extensions of the results to multicast networks, half-duplex networks and ergodic networks.Comment: To appear in IEEE transactions on Information Theory, Vol 57, No 4, April 201

Achievable Rate Regions for Two-Way Relay Channel using Nested Lattice Coding

This paper studies Gaussian Two-Way Relay Channel where two communication nodes exchange messages with each other via a relay. It is assumed that all nodes operate in half duplex mode without any direct link between the communication nodes. A compress-and-forward relaying strategy using nested lattice codes is first proposed. Then, the proposed scheme is improved by performing a layered coding : a common layer is decoded by both receivers and a refinement layer is recovered only by the receiver which has the best channel conditions. The achievable rates of the new scheme are characterized and are shown to be higher than those provided by the decode-and-forward strategy in some regions.Comment: 27 pages, 13 figures, Submitted to IEEE Transactions on Wireless Communications (October 2013