Network Coding over a Noisy Relay : a Belief Propagation Approach

Abstract

In recent years, network coding has been investigated as a method to obtain improvements in wireless networks. A typical assumption of previous work is that relay nodes performing network coding can decode the messages from sources perfectly. On a simple relay network, we design a scheme to obtain network coding gain even when the relay node cannot perfectly decode its received messages. In our scheme, the operation at the relay node resembles message passing in belief propagation, sending the logarithm likelihood ratio (LLR) of the network coded message to the destination. Simulation results demonstrate the gain obtained over different channel conditions. The goal of this paper is not to give a theoretical result, but to point to possible interaction of network coding with user cooperation in noisy scenario. The extrinsic information transfer (EXIT) chart is shown to be a useful engineering tool to analyze the performance of joint channel coding and network coding in the network.

Minimum MSE relaying in coded networks

“…[4,5,3]) these LLRs are simply scaled to the transmit power constraint and then forwarded. This relay function is called Decode-Amplify-Forward (DAF) [3] and the transmitted signal from R p,s to the next relay in this path R p,s+1 can be written as…”

“…This approach called Decode-Amplify-Forward (DAF) was applied e.g. in [3,4,5]. In contrast to this, in [6] so-called soft bits representing the expectation values of the code bits are used, but without a motivation or comparative analysis.…”

A practical joint network-channel coding scheme for reliable communication in wireless networks

“…Bao and Li extended ANCC [5] to GANCC on packet level [2] and presented the general framework that unifies channel coding and network coding. Yang et al and Kang et al further proposed iterative network and channel decoding when the relays cannot perfectly recover packets in [32] and [17] respectively. Nazer et al and Narayanan et al even applied lattice code on relays considering the multi-access property of wireless networks to approach the capacity in [27,26,25].…”

“…However, conventional methods treat them separately, which introduce lots of waste: erasure-correction de- coding cannot take advantage of the redundant information in the packets that fail channel decoding and hence are discarded at the physical layer, while error-correction decoding cannot take advantages of the network layer collaborations. Recently a number of research efforts have tried to unify the two types of coding schemes [5,14,12,2,32,17,27,26,25]. These studies use a simple topology with only one relay, binary channel coding, binary XOR network coding or unpractical physical layer network coding for the sake of easing theoretic analysis.…”

An adaptive compress-and-forward scheme for the orthogonal multiple-access relay channel

“…Design of compression schemes for compress-and-forward in the relay channel with a single source was studied in [10] and [11] with and without Wyner-Ziv coding, respectively. In more recent work [12], the authors combine network coding with analog forwarding of beliefs from the relay achieving notable gains in fixed additive white Gaussian noise (AWGN) channels, which can be improved upon by proper quantization at the relay [13]. Our goal is to introduce a practical, low-complexity, and yet diversity achieving compress-and-forward scheme for the MARC.…”