1536-1276 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TWC.2018.2879486, IEEE Transactions on Wireless Communications 1 Joint Noisy Network Coding and Decode-Forward Relaying for Non-Orthogonal Multiple Access Jawwad Nasar Chattha and Momin Uppal, Senior Member, IEEE Abstract—We consider a non-orthogonal multiple access channel in which multiple users communicate with a base- station through a dedicated relay. For this setup, we propose a novel Joint-NNC-DF cooperation scheme that employs noisy network coded (NNC) relaying with opportunistic decode-and- forward (DF). The proposed scheme utilizes DF cooperation when messages from all user are successfully decoded at the relay and NNC when the relay is unable to decode any one of the users. In the scenario when the relay decodes only a subset of users, the proposed scheme utilizes joint DF and NNC encoding. We derive the information theoretic conditions required for successful message recovery and show that Joint-NNC-DF has a strictly better outage performance than either of the conventional DF- only, NNC-only, or DF-or-NNC schemes. For the two-user case, we derive closed-form expressions for the outage performance under Rayleigh fading while assuming access only to the local channel state information at the relay. These expressions let us choose the NNC quantization parameter so as to attain optimum outage performance. Simulation results validate the theoretical findings and depict that Joint-NNC-DF achieves a performance gain of 0.75 dB, 1.7 dB and 2.1 dB compared to the DF-or-NNC, DF-only and NNC-only strategies, respectively. Index Terms—Non-orthogonal multiple access, relaying, decode-and-forward, noisy network coding. I. I NTRODUCTION Non-orthogonal multiple access (NOMA) is one of the candidate techniques for addressing the envisioned high- throughput massive-connectivity requirements of 5G networks [2]. In this paper, we consider uplink NOMA where multiple users transmit their respective data to a single base-station (BS) via a dedicated relaying node. We refer to this setup as NOMA relaying (NOMAR), a subclass of multiple access relay channels (MARC) initially introduced in [3]. The two prevalent cooperation schemes relevant to our work, originally proposed for the three-node relay network but also applicable to NOMAR, are the so-called decode-forward (DF) and compress-forward (CF) strategies [4]. In DF, the relay attempts to decode the user messages and forwards the re- encoded version to the BS only if decoding is successful. As a result, the source-relay link may become a bottleneck in the DF performance. On the other hand, in CF, the relay does not attempt to decode, but rather compresses This work was supported by the Higher Education Commission of Pakistan under Grant number 5915 of the NRPU program. This paper was presented in part at the IEEE International Conference on Communications (ICC) 2017 [1]. Jawwad Chattha was with the Lahore University of Management Sciences. He is now associated with University of Management and Technology, Lahore, Pakistan, e-mail: 11060022@lums.edu.pk, jawwad.chattha@umt.edu.pk. Momin Uppal is with Lahore University of Management Sciences, Lahore, Pakistan, e-mail: momin.uppal@lums.edu.pk. the noisy signal received from the source using Wyner-Ziv binning [5] and forwards the bin-index to the BS. Over the years, multiple variants of CF relaying have appeared in the literature including the quantize-map-and-forward (QMF) [6] and the noisy network coding (NNC) scheme [7]. The QMF scheme stems from the analysis of a wireless network as a deterministic model, while NNC extends QMF so as to obtain a single letter expression of achievable rate through vector quantization at the relay. NNC bounds are within a tighter gap to the cut-set bound than those of the QMF scheme which employs scalar quantization [8]. Moreover, NNC does away with Wyner-Ziv binning and is based on joint decoding of user messages without explicit decoding of the compression indices. As a result, NNC is beneficial over CF in practical fading type of scenarios [7] in which the relay does not have access to the global channel state information (CSI). For the NOMAR setup, each user experiences a different channel quality to the relay. As a result, the relay may be able to decode all, none or only a subset of the users. When all user messages are decoded at the relay, the most natural choice for the relay is to utilize DF cooperation. On the other end is the case when none of the messages is successfully recovered, for which NNC is a reasonable choice. A more likely and important scenario though is when only a subset of user messages are successfully recovered at the relay. In this paper, we propose a novel Joint-NNC-DF (J-NNC-DF) scheme for the NOMAR, in which the relay utilizes a single codebook that jointly (a) encodes the successfully decoded messages and (b) applies NNC to the noisy signal corresponding to the users whose messages remained unrecoverable. The proposed J-NNC-DF scheme falls under the category of hybrid or mixed relaying schemes. Relevant works in the domain include [9] that presents a combination of DF and NNC for a three node network consisting of a transmitter-receiver pair aided by a dedicated relay. Authors consider splitting user message into a common and a private message which are superposition coded before transmission. The common message is different in each block and is decoded at the relay and BS as in DF, while the private message is the same for all blocks and is decoded only at the destination as in NNC. Similarly, [10] proposes superposition coding for the rate-split message but presents the generalized achievable rates for multiple-source multicast networks. This work also indicates higher achievable rates of the proposed scheme compared to NNC-only or CF- only relaying. In [11], the authors propose the use of NNC with DF through rate-splitting. This proposed relaying scheme highlights the interference limitation of a mixed scheme which is mitigated through the use of short-NNC relaying. A