## 1 Introduction  
Cloud radio access network (C-RAN) systems have a potential of reducing the capital and operating expenditures and of improving spectral and energy efficiency. These benefits can be realized by centralized baseband signal processing at baseband processing unit (BBU) pools [1; 2; 3]. However, it is challenging to reliably transfer baseband samples on fronthaul links that connect distributed radio units (RUs) to nearby BBUs particularly for broadband communication systems. To address this issue, the authors of [4; 5] proposed efficient compression techniques which can effectively reduce the fronthaul overhead by exploiting signal correlation among distributed RUs. Signal processing design of fronthaul-constrained C-RAN systems has also been studied in more complicated C-RAN systems that are equipped with multi-hop fronthaul networks [6] or with spectrum pooling capability among network operators [7]. Another challenge to implement C-RAN is that it is not trivial to mitigate the impact of interference signals among nearby clusters, where each cluster consists of a set of RUs and users that are served by a single BBU. Dynamic clustering approaches based on instantaneous channel state information (CSI) were proposed and analyzed in [8; 9]. For given clusters, the authors of [10] addressed inter-cluster coordinated design of downlink precoding and fronthaul compression strategies, and investigated the advantages of inter-cluster coordinated design compared to inter-cluster time-division multiple access (TDMA) or intra-cluster design which neglects the impact of inter-cluster interference signals. In this work, we propose an inter-cluster, or inter-BBU, cooperative reception strategy that aims at mitigating the impact of inter-cluster interference signals in the uplink of C-RAN systems. We consider a practical inter-cluster cooperation model, in which the BBUs of two nearby clusters exchange the information of in-cluster uplink baseband signals on finite-capacity backhaul links. In the conventional inter-BBU cooperation scheme proposed in [7], each RU produces a single quantized signal, or single description, and one needs to decide the set of RUs whose quantized signals are transferred not only to the serving BBU but also to the neighboring BBU. The optimization of this scheme asks for a discrete search of exponentially increasing search size with respect to the number of RUs. Motivated by this issue, we propose a layered compression strategy at RUs, whereby each RU produces two quantized signals that are decompressed only by the serving BBU or both by the serving and neighboring BBUs, and the compression rate allocation among the two descriptions is included to the design space. With this approach, we can efficiently utilize the fronthaul and backhaul links without resorting to a discrete search. Similar approaches were studied in [11; 12] that adopt a layered compression strategy for robust exploitation of packet-based fronthaul networks [11] or for flexible inter-user cooperation [12]. It was reported by [11] that multiple description coding can outperform traditional packet diversity techniques in terms of efficiently utilizing multiple routes, which are subject to independent congestion and packet losses, in packet-based multi-hop fronthaul networks. [12] investigated the advantages of broadcast coding and layered compression under the scenario of inter-user cooperation, in which a user informs multiple users through a broadcast channel with different channel gains across receiving users. We note that in the studies of [11; 12], multiple description coding was used to enable compression fidelity to be adapted to different packet loss events or different channel gains. Unlike those, in this work, we adopt multiple description coding with the aim of making the quality of the quantized signals decompressed at serving and neighboring BBUs different from each other, since the RU-to-BBU fronthaul and inter-BBU backhaul links can have different capacity. The paper is organized as follows.