The compute-and-forward framework permits each receiver in a Gaussian network to directly decode a linear combination of the transmitted messages. The resulting linear combinations can then be employed as an end-to-end communication strategy for relaying, interference alignment, and other applications. Recent efforts have demonstrated the advantages of employing unequal powers at the transmitters and decoding more than one linear combination at each receiver. However, neither of these techniques fit naturally within the original formulation of compute-and-forward. This paper proposes an expanded compute-and-forward framework that incorporates both of these possibilities and permits an intuitive interpretation in terms of signal levels. Within this framework, recent achievability and optimality results are unified and generalized.
In recent, independent work, Zhu and Gastpar @cite_55 proposed a compute-and-forward scheme for unequal powers based on the scheme of @cite_60 . They also showed how to use this scheme to reach the two-user multiple-access sum capacity (if the channel strength lies above a small constant). However, their scheme does not retain the connection to a finite field.
@cite_55 @cite_60
2400872280 1505858209
This paper studies the uplink of a cloud radio access network (C-RAN) where the cell sites are connected to a cloud-computing-based central processor (CP) with noiseless backhaul links with finite capacities. We employ a simple compress-and-forward scheme in which the base stations (BSs) quantize the received signals and send the quantized signals to the CP using either distributed Wyner-Ziv coding or single-user compression. The CP first decodes the quantization codewords and then decodes the user messages as if the remote users and the cloud center form a virtual multiple-access channel (VMAC). This paper formulates the problem of optimizing the quantization noise levels for weighted sum rate maximization under a sum backhaul capacity constraint. We propose an alternating convex optimization approach to find a local optimum solution to the problem efficiently, and more importantly, to establish that setting the quantization noise levels to be proportional to the background noise levels is near optimal for sum-rate maximization when the signal-to-quantization-noise-ratio (SQNR) is high. In addition, with Wyner-Ziv coding, the approximate quantization noise level is shown to achieve the sum-capacity of the uplink C-RAN model to within a constant gap. With single-user compression, a similar constant-gap result is obtained under a diagonal dominant channel condition. These results lead to an efficient algorithm for allocating the backhaul capacities in C-RAN. The performance of the proposed scheme is evaluated for practical multicell and heterogeneous networks. It is shown that multicell processing with optimized quantization noise levels across the BSs can significantly improve the performance of wireless cellular networks. We consider a distributed antenna system where L antenna terminals (ATs) are connected to a Central Processor (CP) via digital error-free links of finite capacity R 0 , and serve K user terminals (UTs). This system model has been widely investigated both for the uplink and the downlink, which are instances of the general multiple-access relay and broadcast relay networks. In this work we focus on the downlink, and propose a novel downlink precoding scheme nicknamed “Reverse Quantized Compute and Forward”(RQCoF). For this scheme we obtain achievable rates and compare with the state-of-the-art available in the literature. We also provide simulation results for a realistic network with fading with K > L UTs, and show that channel-based user selection produces large benefits and essentially removes the problem of rank deficiency in the system matrix.1 In this paper, the role of cooperation in managing interference-a fundamental feature of the wireless channel-is investigated by studying the two-user Gaussian interference channel where the source nodes can both transmit and receive in full duplex. The sum capacity of this channel is obtained within a gap of a constant number of bits. The coding scheme used builds up on the superposition scheme of Han and Kobayashi for the two-user interference channel without cooperation. New upperbounds on the sum capacity are also derived. The same coding scheme is shown to obtain the sum capacity of the symmetric two-user Gaussian interference channel with noiseless feedback within a constant gap. In a recent work, Nazer and Gastpar proposed the compute-and-forward strategy as a physical-layer network coding scheme. They described a code structure based on nested lattices whose algebraic structure makes the scheme reliable and efficient. In a more recent paper, Niesen and Whiting revealed a fundamental limitation of the decoder used by Nazer and Gastpar. In this work, we consider maximum-likelihood decoding of compute-and-forward, aiming to overcome its limitation. By examining the decoding metric from the viewpoint of Gaussian measures over lattices, we present a design criterion of the lattice code based on the flatness factor, and propose a new decoding algorithm based on inhomogeneous Diophantine approximation. The multiuser communication channel, in which multiple users exchange information with the help of a relay terminal, termed the multiway relay channel (mRC), is introduced. In this model, multiple interfering clusters of users communicate simultaneously, such that the users within the same cluster wish to exchange messages among themselves, i.e., each user multicasts its message to all the other users in its own cluster. It is assumed that the users cannot receive each other's signals directly. Hence, the relay terminal in this model is the enabler of communication. In particular, restricted encoders are considered, such that the encoding function of each user depends only on its own message and the received signal is used only for decoding the messages of the other users in the cluster. Achievable rate regions and an outer bound are characterized for the Gaussian mRC, and their comparison is presented in terms of the exchange rate, the symmetric rate point in the capacity region in a symmetric Gaussian mRC scenario. It is shown that the compress-and-forward (CF) protocol achieves exchange rates within a constant bit offset of the optimal exchange rate, independent of the power constraints of the terminals in the network. A finite bit gap between the exchange rates achieved by the CF and the amplify-and-forward protocols is also shown. The two special cases of the mRC, the full data exchange model, in which every user wants to receive messages of all other users, and the pairwise data exchange model which consists of multiple two-way relay channels, are investigated in detail. In particular for the pairwise data exchange model, in addition to the proposed random coding-based achievable schemes, a nested lattice coding-based scheme is also presented and is shown to achieve exchange rates within a constant bit gap of the exchange capacity. We study a distributed antenna system where L antenna terminals (ATs) are connected to a central processor (CP) via digital error-free links of finite capacity R0, and serve K user terminals (UTs). This model has been widely investigated both for the uplink (UTs to CP) and for the downlink (CP to UTs), which are instances of the general multiple-access relay and broadcast relay networks. We contribute to the subject in the following ways: 1) For the uplink, we consider the recently proposed “compute and forward” (CoF) approach and examine the corresponding system optimization at finite SNR. 2) For the downlink, we propose a novel precoding scheme nicknamed “reverse compute and forward” (RCoF). 3) In both cases, we present low-complexity versions of CoF and RCoF based on standard scalar quantization at the receivers, that lead to discrete-input discrete-output symmetric memoryless channel models for which near-optimal performance can be achieved by standard single-user linear coding. 4) We provide extensive numerical results and finite SNR comparison with other “state of the art” information theoretic techniques, in scenarios including fading and shadowing. The proposed uplink and downlink system optimization focuses specifically on the ATs and UTs selection problem. In both cases, for a given set of transmitters, the goal consists of selecting a subset of the receivers such that the corresponding system matrix has full rank and the sum rate is maximized. We present low-complexity ATs and UTs selection schemes and demonstrate through Monte Carlo simulation that the proposed schemes essentially eliminate the problem of rank deficiency of the system matrix and greatly mitigate the noninteger penalty affecting CoF RCoF at high SNR. Comparison with other state-of-the art information theoretic schemes, show competitive performance of the proposed approaches with significantly lower complexity. This paper investigates the compress-and-forward scheme for an uplink cloud radio access network (C-RAN) model, where multi-antenna base stations (BSs) are connected to a cloud-computing-based central processor (CP) via capacity-limited fronthaul links. The BSs compress the received signals with Wyner-Ziv coding and send the representation bits to the CP; the CP performs the decoding of all the users’ messages. Under this setup, this paper makes progress toward the optimal structure of the fronthaul compression and CP decoding strategies for the compress-and-forward scheme in the C-RAN. On the CP decoding strategy design, this paper shows that under a sum fronthaul capacity constraint, a generalized successive decoding strategy of the quantization and user message codewords that allows arbitrary interleaved order at the CP achieves the same rate region as the optimal joint decoding. Furthermore, it is shown that a practical strategy of successively decoding the quantization codewords first, then the user messages, achieves the same maximum sum rate as joint decoding under individual fronthaul constraints. On the joint optimization of user transmission and BS quantization strategies, this paper shows that if the input distributions are assumed to be Gaussian, then under joint decoding, the optimal quantization scheme for maximizing the achievable rate region is Gaussian. Moreover, Gaussian input and Gaussian quantization with joint decoding achieve to within a constant gap of the capacity region of the Gaussian multiple-input multiple-output (MIMO) uplink C-RAN model. Finally, this paper addresses the computational aspect of optimizing uplink MIMO C-RAN by showing that under fixed Gaussian input, the sum rate maximization problem over the Gaussian quantization noise covariance matrices can be formulated as convex optimization problems, thereby facilitating its efficient solution. In this paper, we consider a class of single-source multicast relay networks. We assume that all outgoing channels of a node in the network to its neighbors are orthogonal while the incoming signals from its neighbors can interfere with each other. We first focus on Gaussian relay networks with interference and find an achievable rate using a lattice coding scheme. We show that the achievable rate of our scheme is within a constant bit gap from the information theoretic cut-set bound, where the constant depends only on the network topology, but not on the transmit power, noise variance, and channel gains. This is similar to a recent result by Avestimehr, Diggavi, and Tse, who showed an approximate capacity characterization for general Gaussian relay networks. However, our achievability uses a structured code instead of a random one. Using the idea used in the Gaussian case, we also consider a linear finite-field symmetric network with interference and characterize its capacity using a linear coding scheme. This paper considers the optimal uplink transmission strategy that achieves the sum-capacity in a multiuser multi-antenna wireless system. Assuming an independent identically distributed block-fading model with transmitter channel side information, beamforming for each remote user is shown to be necessary for achieving sum-capacity when there is a large number of users in the system. This result stands even in the case where each user is equipped with a large number of transmit antennas, and it can be readily extended to channels with intersymbol interference if an orthogonal frequency division multiplexing modulation is assumed. This result is obtained by deriving a rank bound on the transmit covariance matrices, and it suggests that all users should cooperate by each user using only a small portion of available dimensions. Based on the result, a suboptimal transmit scheme is proposed for the situation where only partial channel side information is available at each transmitter. Simulations show that the suboptimal scheme is not only able to achieve a sum rate very close to the capacity, but also insensitive to channel estimation error. This paper considers the transmitter design for wireless information and energy transfer (WIET) in a multiple-input single-output (MISO) interference channel (IFC). The design problem is to maximize the system throughput subject to individual energy harvesting constraints and power constraints. It is observed that the ideal scheme, where the receivers simultaneously perform information detection (ID) and energy harvesting (EH) from the received signal, may not always achieve the best tradeoff between information transfer and energy harvesting, but simple practical schemes based on time splitting may perform better. We therefore propose two practical time splitting schemes, namely the time-division mode switching (TDMS) and time-division multiple access (TDMA), in addition to the existing power splitting (PS) scheme. In the two-user scenario, we show that beamforming is optimal to all the schemes. Moreover, the design problems associated with the TDMS and TDMA schemes admit semi-analytical solutions. In the general K-user scenario, a successive convex approximation method is proposed to handle the WIET problems associated with the ideal scheme, the PS scheme and the TDMA scheme, which are known NP-hard in general. Simulation results show that none of the schemes under consideration can always dominate another in terms of the sum rate performance. Specifically, it is observed that stronger cross-link channel power improves the achievable sum rate of time splitting schemes but degrades the sum rate performance of the ideal scheme and PS scheme. As a result, time splitting schemes can outperform the ideal scheme and the PS scheme in interference dominated scenarios. In this paper, we study the resource allocation and user scheduling problem for a downlink non-orthogonal multiple access network where the base station allocates spectrum and power resources to a set of users. We aim to jointly optimize the sub-channel assignment and power allocation to maximize the weighted total sum-rate while taking into account user fairness. We formulate the sub-channel allocation problem as equivalent to a many-to-many two-sided user-subchannel matching game in which the set of users and sub-channels are considered as two sets of players pursuing their own interests. We then propose a matching algorithm, which converges to a two-side exchange stable matching after a limited number of iterations. A joint solution is thus provided to solve the sub-channel assignment and power allocation problems iteratively. Simulation results show that the proposed algorithm greatly outperforms the orthogonal multiple access scheme and a previous non-orthogonal multiple access scheme. The problem of designing physical-layer network coding (PNC) schemes via nested lattices is considered. Building on the compute-and-forward (C&F) relaying strategy of Nazer and Gastpar, who demonstrated its asymptotic gain using information-theoretic tools, an algebraic approach is taken to show its potential in practical, nonasymptotic, settings. A general framework is developed for studying nested-lattice-based PNC schemes-called lattice network coding (LNC) schemes for short-by making a direct connection between C&F and module theory. In particular, a generic LNC scheme is presented that makes no assumptions on the underlying nested lattice code. C&F is reinterpreted in this framework, and several generalized constructions of LNC schemes are given. The generic LNC scheme naturally leads to a linear network coding channel over modules, based on which noncoherent network coding can be achieved. Next, performance complexity tradeoffs of LNC schemes are studied, with a particular focus on hypercube-shaped LNC schemes. The error probability of this class of LNC schemes is largely determined by the minimum intercoset distances of the underlying nested lattice code. Several illustrative hypercube-shaped LNC schemes are designed based on Constructions A and D, showing that nominal coding gains of 3 to 7.5 dB can be obtained with reasonable decoding complexity. Finally, the possibility of decoding multiple linear combinations is considered and related to the shortest independent vectors problem. A notion of dominant solutions is developed together with a suitable lattice-reduction-based algorithm. We generalize the Gel'fand-Pinsker model to encompass the setup of a memoryless multiple-access channel (MAC). According to this setup, only one of the encoders knows the state of the channel (noncausally), which is also unknown to the receiver. Two independent messages are transmitted: a common message and a message transmitted by the informed encoder. We find explicit characterizations of the capacity region with both noncausal and causal state information. Further, we study the noise-free binary case, and we also apply the general formula to the Gaussian case with noncausal channel state information, under an individual power constraint as well as a sum power constraint. In this case, the capacity region is achievable by a generalized writing-on-dirty-paper scheme. A noisy network coding scheme for communicating messages between multiple sources and destinations over a general noisy network is presented. For multi-message multicast networks, the scheme naturally generalizes network coding over noiseless networks by Ahlswede, Cai, Li, and Yeung, and compress-forward coding for the relay channel by Cover and El Gamal to discrete memoryless and Gaussian networks. The scheme also extends the results on coding for wireless relay networks and deterministic networks by Avestimehr, Diggavi, and Tse, and coding for wireless erasure networks by Dana, Gowaikar, Palanki, Hassibi, and Effros. The scheme involves lossy compression by the relay as in the compress-forward coding scheme for the relay channel. However, unlike previous compress-forward schemes in which independent messages are sent over multiple blocks, the same message is sent multiple times using independent codebooks as in the network coding scheme for cyclic networks. Furthermore, the relays do not use Wyner-Ziv binning as in previous compress-forward schemes, and each decoder performs simultaneous decoding of the received signals from all the blocks without uniquely decoding the compression indices. A consequence of this new scheme is that achievability is proved simply and more generally without resorting to time expansion to extend results for acyclic networks to networks with cycles. The noisy network coding scheme is then extended to general multi-message networks by combining it with decoding techniques for the interference channel. For the Gaussian multicast network, noisy network coding improves the previously established gap to the cutset bound. We also demonstrate through two popular Gaussian network examples that noisy network coding can outperform conventional compress-forward, amplify-forward, and hash-forward coding schemes. In this paper, we investigate the impact of limited backhaul capacity on user scheduling in the context of a heterogeneous network comprising a macro base station overlaid with small-cells. Under a global proportional fairness (PF) criteria, we show that this limited capacity has a fundamental impact on user scheduling. When user association and channel allocation are given, like in the infinite-capacity backhaul case, the global PF user scheduling problem can be decomposed into a set of independent local PF user scheduling problems. However, unlike the case with infinite backhaul where the local PF scheme is equivalent to giving equal time to each user, a local PF scheme with finite backhaul can be of one of three types. We completely characterize these three types and the conditions under which to use them. The results show that a backhaul-aware scheduling scheme is simple to implement and necessary to obtain the best performance. We consider an uncoordinated Gaussian multiple access channel with a relatively large number of active users within each block. A low complexity coding scheme is proposed, which is based on a combination of compute-and-forward and coding for a binary adder channel. For a wide regime of parameters of practical interest, the energy-per-bit required by each user in the proposed scheme is significantly smaller than that required by popular solutions such as slotted-ALOHA and treating interference as noise. Space-time network coding (STNC) is a time-division multiple access (TDMA)-based scheme that combines network coding and space-time coding by allowing relay nodes to combine the information received from different source nodes during the transmission phase and to forward the combined signal to a destination node in the relaying phase. However, STNC schemes require all the relay nodes to overhear the signals transmitted from all the source nodes in the network. They also require a large number of time-slots to achieve full diversity in a multipoint-to-multipoint transmission. Both conditions are particularly challenging for large cellular networks where, assuming a downlink transmission, base stations (BSs) and users only overhear a subset of all the BSs. In this paper, we exploit basic knowledge of the network topology in order to reduce the number of time-slots by allowing simultaneous transmissions from those BSs that do not overhear each other. Our results show that these topology-aware schemes are able to increase the spectral efficiency per time-slot and bit error rate with unequal transmit power and channel conditions. This paper studies an uplink multicell joint processing model in which the base-stations are connected to a centralized processing server via rate-limited digital backhaul links. We propose a simple scheme that performs Wyner-Ziv compress-and-forward relaying on a per-base-station basis followed by successive interference cancellation (SIC) at the central processor. The proposed scheme has a significantly reduced complexity as compared to joint decoding, resulting in an easily computable achievable rate region. Although suboptimal in general, this paper shows that the proposed per-base-station SIC scheme can achieve the sum capacity of a class of Wyner cellular model to within a constant gap. This paper also establishes that in order to achieve to within a constant gap to the maximum SIC rate with infinite backhaul, the limited-backhaul system must have backhaul capacities that scale logarithmically with the signal-to-interference-and-noise ratios (SINRs) at the base-stations. Further, this paper studies the optimal backhaul rate allocation problem for the per-base-station SIC model with a total backhaul capacity constraint, and shows that the sum-rate maximizing allocation should also have individual backhaul rates that scale logarithmically with the SINR at each base-station. Finally, the proposed per-base-station SIC scheme is evaluated in a practical multicell network to quantify the performance gain brought by multicell processing. Orthogonal Frequency Division Multiple Access (OFDMA) as well as other orthogonal multiple access techniques fail to achieve the system capacity limit in the uplink due to the exclusivity in resource allocation. This issue is more prominent when fairness among the users is considered in the system. Current Non-Orthogonal Multiple Access (NOMA) techniques introduce redundancy by coding spreading to facilitate the users' signals separation at the receiver, which degrade the system spectral efficiency. Hence, in order to achieve higher capacity, more efficient NOMA schemes need to be developed. In this paper, we propose a NOMA scheme for uplink that removes the resource allocation exclusivity and allows more than one user to share the same subcarrier without any coding spreading redundancy. Joint processing is implemented at the receiver to detect the users' signals. However, to control the receiver complexity, an upper limit on the number of users per subcarrier needs to be imposed. In addition, a novel subcarrier and power allocation algorithm is proposed for the new NOMA scheme that maximizes the users' sum-rate. The link-level performance evaluation has shown that the proposed scheme achieves bit error rate close to the single-user case. Numerical results show that the proposed NOMA scheme can significantly improve the system performance in terms of spectral efficiency and fairness comparing to OFDMA. As one of the key technologies for future wireless communication systems, user cooperation has a great potential in improving the system performance. In this paper, the diversity benefit of user cooperation is evaluated using diversity-multiplexing tradeoff (DMT) as the performance metric. Ways of exploiting the diversity benefit are devised. We investigate two typical channel models, namely, the multiple-access channel (MAC) and the interference channel (IFC). For the MAC, all the terminals are equipped with multiple antennas and the K(K ≥ 2) sources cooperate in a full-duplex mode. We determine the optimal DMT of the channel and propose a compressed-and-forward (CF) based cooperation scheme to achieve the optimal DMT. For the IFC, we consider a two-user channel with single-antenna terminals and full-duplex source cooperation. A DMT upper bound and two DMT lower bounds are derived. The upper bound is derived based on a channel capacity upper bound, and the lower bounds are derived using decode-and-forward (DF) based cooperation schemes. In most channel scenarios, the bounds are found to be tight. This implies that under certain channel scenarios, the optimal DMT of the channel can be achieved by DF-based cooperation schemes.