Multiuser Cooperative Diversity Through Network Coding Based on Classical Coding Theory

Abstract

Abstract-In this work, we propose and analyze a generalized construction of distributed network codes for a network consisting of M users sending different information to a common base station through independent block fading channels. The aim is to increase the diversity order of the system without reducing its throughput. The proposed scheme, called generalized dynamicnetwork codes (GDNC), is a generalization of the dynamicnetwork codes (DNC) recently proposed by Xiao and Skoglund. The design of the network codes that maximize the diversity order is recognized as equivalent to the design of linear block codes over a nonbinary finite field under the Hamming metric. We prove that adopting a systematic generator matrix of a maximum distance separable block code over a sufficiently large finite field as the network transfer matrix is a sufficient condition for full diversity order under link failure model. The proposed generalization offers a much better tradeoff between rate and diversity order compared to the DNC. An outage probability analysis showing the improved performance is carried out, and computer simulations results are shown to agree with the analytical results.Index Terms-Cooperative communication, diversity order, nonbinary network coding, Singleton bound.

Flexible Network Codes Design for Cooperative Diversity

“…Upon reception of y S 1 R 1 , y S 1 R 2 , y S 2 R 1 , and y S 2 R 2 , the relays R 1 and R 2 attempt to decode the symbols transmitted by S 1 and S 2 in a similar fashion as in a Decode-and-Forward (DF) cooperative protocol (Scaglione et al, 2006). Unlike other solutions available in the literature for network code design for cooperative networks (Xiao & Skoglund, 2009a) (Xiao & Skoglund, 2009b), (Rebelatto et al, 2010a), (Rebelatto et al, 2010b), we do not rely on powerful (i.e., Shannon-like) channel codes at the physical layer, which allow each relay to detect correct and wrong packets, and enable them to forward only the former ones. We consider a very simple implementation in which the relays demodulate-network-code-and-forward (D-NC-F) each received symbol without checking whether the symbol is correct or wrong.…”

“…This scenario corresponds to using a distributed network code obtained from a (4, 2, 2) UEP code (Van Gils, 1983, Table I), where a higher diversity gain has to be assigned to source S 1 . Scenario 1 and Scenario 2 correspond to state-of-the-art distributed coding techniques (Rebelatto et al, 2010b), while Scenario 3 and Scenario 4 are the flexible network codes we are interested in studying in this book chapter. The reason why UEP coding theory can be a suitable tool to design distributed network codes for application scenarios in which different sources require a different diversity gain (see also Section 1) has its information-theoretic foundation in (Zhang, 2008).…”

“…As a matter of fact, the application of NC to a wireless context needs to take into account that the wireless medium is highly unpredictable and inhospitable for adopting the existing NC algorithms, which have mostly been designed by assuming wired (i.e., error-free) out that max-diversity-achieving network codes can be obtained by resorting to the theory of non-binary linear block codes. For example, as far as the canonical two-source two-relay cooperative network is concerned, the methods proposed in (Xiao & Skoglund, 2009a), (Xiao & Skoglund, 2009b), (Rebelatto et al, 2010a), (Rebelatto et al, 2010b) can achieve full-diversity, when, instead, XOR-based binary NC (Katti et al, 2008a) cannot. The solution proposed by all these papers to overcome the limitation in the achievable diversity is based on using network codes in a non-binary Galois field.…”

“…However, the price to be paid for this performance improvement is the additional complexity required at the relay nodes, which must network-code the received packets by using non-binary arithmetic. Also, longer decoding delays are, in general, required to design full-diversity-achieving network codes (Rebelatto et al, 2010b). Furthermore, the solutions available in (Xiao & Skoglund, 2009a), (Xiao & Skoglund, 2009b), Rebelatto et al (2010a), (Rebelatto et al, 2010b) aim at guaranteeing the same diversity gain for all the active sources of the network, which, in general, leads to an inflexible network code design as multiple sources might have different Quality-of-Service (QoS) requirements, and, so, might need different diversity gains.…”

“…Also, longer decoding delays are, in general, required to design full-diversity-achieving network codes (Rebelatto et al, 2010b). Furthermore, the solutions available in (Xiao & Skoglund, 2009a), (Xiao & Skoglund, 2009b), Rebelatto et al (2010a), (Rebelatto et al, 2010b) aim at guaranteeing the same diversity gain for all the active sources of the network, which, in general, leads to an inflexible network code design as multiple sources might have different Quality-of-Service (QoS) requirements, and, so, might need different diversity gains. In conclusion, the solutions available so far seem to be still inflexible to accommodate the needs of the multi-source multi-relay scenario, as well as to keep the computational complexity of the relay nodes at a low level.…”