Gaussian Multiple Access Channel Research Articles

Capacity Bounds for a Class of Diamond Networks With Conferencing Relays

Diamond channels can model modern wireless communication infrastructure that use relays to increase network capacity. This letter investigates the effect of conferencing between the relays in a particular class of diamond networks with source-to-relay and conferencing channels modeled as noiseless bit-pipes of given capacities. A lower bound to the capacity for this network and an upper bound that is tighter than the cut-set bound are presented. Such networks with specific multiple access channel (MAC) types are studied and the minimum conferencing link capacity needed to achieve full cooperation for each MAC is ascertained. It is found that such minimum conferencing link capacity for the Gaussian MAC must be equal to the difference between the full cooperation capacity and the backhaul capacity. However, such a result does not hold in general as the binary adder MAC illustrates a counterexample.

Second-Order Asymptotics for the Gaussian MAC With Degraded Message Sets

This paper studies the second-order asymptotics of the Gaussian multiple-access channel with degraded message sets. For a fixed average error probability $\varepsilon \in (0,1)$ and an arbitrary point on the boundary of the capacity region, we characterize the speed of convergence of rate pairs that converge to that boundary point for codes that have asymptotic error probability no larger than $\varepsilon$. As a stepping stone to this local notion of second-order asymptotics, we study a global notion, and establish relationships between the two. We provide a numerical example to illustrate how the angle of approach to a boundary point affects the second-order coding rate. This is the first conclusive characterization of the second-order asymptotics of a network information theory problem in which the capacity region is not a polygon.

On the Secrecy Rate Region of Multiple-Access Wiretap Channel With Noncausal Side Information

In this paper, we study the two transmitter multiple-access channel (MAC) with noncausal side information at one (single-sided) or both (two-sided) of the encoders in the presence of an external wiretapper (WT) and under individual and collective secrecy constraints. Our work consists of four parts. First, we consider the discrete memoryless (DM-MAC-WT) case of the model and derive inner and outer bounds on the secrecy capacity region under both of the secrecy constraints. Second, the results are extended to the Gaussian memoryless case [Gaussian multiple-access channel WT (GMAC-WT)] in detail and are used to illustrate numerically that the secrecy rate region is enlarged by increasing the power of the interference signal which is known noncausally at the encoder. Third, we analyze the strong interference regime as an important regime in GMAC with side information and show that under collective secrecy constraint, we can achieve the secrecy capacity region of the single-sided channel asymptotically for a special case in which the signal and noise powers satisfy specific constraints. To the best of our knowledge, this capacity region is the first one obtained for GMAC-WT. Finally, we show that our results include previous works as its special cases for both the single-sided and two-sided channel models.

Duality Between the Improved Rate Regions of Gaussian Multiple Access and Broadcast Channel for Discrete Constellations

In this paper, we first look at the achievable rate regions of the Gaussian Multiple Access Channel (G-MAC) and Gaussian Broadcast Channel (G-BC) when discrete constellations are transmitted. Focusing on the two-user case and assuming uncoded Pulse Amplitude Modulation (PAM), we show that the rate regions of G-MAC and G-BC can be improved by power conservation at the transmitter, a factor ignored in the earlier derived rate regions. We then further investigate duality between the G-MAC and the G-BC and show that a rate pair achieved in the G-MAC can be translated to a rate pair in the dual G-BC, such that the equal sum power constraint be satisfied. Due to the similarity of the rate expressions to Shannon's capacity formula, for an appropriate choice of signal to noise ratio (SNR) gap, we show that when finite constellations are used for transmission, rate regions of these two channels also have a dual relationship (the known for Gaussian alphabets). The rate region of the G-BC can therefore be characterized from the rate region of the dual G-MAC and vice versa.

Cooperative multiple access in cognitive radios to enhance QoS for cell edge primary users: asynchronous algorithm and convergence

Cognitive radio (CR) systems have been proposed for efficient usage of spare spectrum licensed to primary systems. This leads to the issue of providing as much spectrum to CR users as possible while not degrading the quality of service (QoS) of primary users of the spectrum. This paper proposes a novel cooperation scheme between primary and CR users to guarantee QoS of primary users up to the cell edge while making the licensed spectrum available for opportunistic access by the CR users. We suggest that the primary users at the cell edge, who have poor QoS, should allow secondary users to access their spectrum, while at the same time, the secondary users would help to enhance the primary users QoS using superposition coding on the primary users transmissions. Thus the proposed method can provide a so called "win-win strategy" by benefiting both primary and CR users. The proposed cooperative access scheme in cognitive radios solves efficiently the sum-rate maximization problem on cognitive Gaussian Multiple Access Channels (GMACs) for power allocation of primary systems that cooperates with CR systems in a distributed fashion. We solved the problem using iterative Jacobian method in a distributed manner. A totally asynchronous distributed power allocation for sum-rate maximization on cognitive GMACs is suggested. Numerical results show that the QoS of primary users at the cell edge is improved by the proposed cooperative access scheme.

Steepest-Descent Optimization of CDMA Signatures for Multiple Correlated Sources With Applications to Joint Source-Channel Coding

An approach to transmitting multiple correlated sources over a Gaussian multiple-access channel (GMAC) using code-division multiple-access (CDMA) is investigated. A block coordinate descent (BCD) algorithm is presented which can be used to optimize CDMA signatures for a given source covariance matrix under individual transmitter power constraints. This algorithm can be used to design non-orthogonal CDMA signatures for GMACs with arbitrary input alphabets, fading, and colored noise. While the main focus has been the design of signatures which minimize the mean square error (MSE) of linear decoding, the algorithm can also be used to design signatures which maximize the input-output mutual information of the channel. This paper investigates the uncoded transmission of Gaussian sources and the coded transmission of binary sources over a GMAC using joint source-channel (JSC) optimized CDMA signatures under constraints on transmitter power and channel bandwidth, scenarios relevant to wireless sensor networks. By using simple coding schemes which only rely on linear multi-user detection and independent channel decoding of a large number of sources, it is demonstrated that CDMA-based JSC coding can exploit inter-source correlation to achieve lower distortion (Gaussian sources) or higher rates (binary sources) compared to conventional separate source-channel (SSC) coding over the same channel bandwidth.

Nomographic Functions: Efficient Computation in Clustered Gaussian Sensor Networks

In this paper, a clustered wireless sensor network is considered that is modeled as a set of coupled Gaussian multiple-access channels. The objective of the network is not to reconstruct individual sensor readings at designated fusion centers but rather to reliably compute some functions thereof. Our particular attention is on real-valued functions that can be represented as a post-processed sum of pre-processed sensor readings. Such functions are called nomographic functions and their special structure permits the utilization of the interference property of the Gaussian multiple-access channel to reliably compute many linear and nonlinear functions at significantly higher rates than those achievable with standard schemes that combat interference. Motivated by this observation, a computation scheme is proposed that combines a suitable data pre- and post-processing strategy with a nested lattice code designed to protect the sum of pre-processed sensor readings against the channel noise. After analyzing its computation rate performance, it is shown that at the cost of a reduced rate, the scheme can be extended to compute every continuous function of the sensor readings in a finite succession of steps, where in each step a different nomographic function is computed. This demonstrates the fundamental role of nomographic representations.

Resource Allocation for Multiple Access Channel With Conferencing Links and Shared Renewable Energy Sources

This paper investigates the resource allocation problem for the Gaussian multiple access channel (MAC) with conferencing links, where the two transmitters can talk to each other via wired rate-limited channels. Moreover, the two transmitters are powered by a shared energy harvester which captures energy from the environment. We consider both the non-causal (the energy arrival levels at future time slots are known before transmissions) and the causal (only the energy arrival levels of past and present slots are known) energy-harvesting (EH) models. For the non-causal case, we formulate a resource allocation problem over a finite horizon of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> time slots to characterize the boundary of the maximum departure region. We then develop the optimal offline power and rate allocation scheme by exploiting the hidden convexity of this problem. Interestingly, it is shown that there exists a maximum transmission rate (named the capping rate) for one of the transmitters. For the causal case, we examine the performance of the greedy scheme, in which the energy is depleted within each slot. In particular, we measure the utility of this scheme against the optimal offline one by competitive analysis, where the competitive ratio of the online greedy scheme, i.e., the maximum ratio between the profits obtained by the offline and online schemes over arbitrary energy arrival profiles, is derived.

Matched Multiuser Gaussian Source Channel Communications via Uncoded Schemes

We investigate whether uncoded schemes are optimal for Gaussian sources on multiuser Gaussian channels. Particularly, we consider two problems: the first is to send correlated Gaussian sources on a Gaussian broadcast channel where each receiver is interested in reconstructing only one source component (or one specific linear function of the sources) under the mean squared error distortion measure; the second is to send correlated Gaussian sources on a Gaussian multiple-access channel, where each transmitter observes a noisy combination of the source, and the receiver wishes to reconstruct the individual source components (or individual linear functions) under the mean squared error distortion measure. It is shown that when the channel parameters match certain general conditions, the induced distortion tuples are on the boundary of the achievable distortion region, and thus optimal. Instead of following the conventional approach of attempting to characterize the achievable distortion region, we ask the question whether and how a match can be effectively determined. This decision problem formulation helps to circumvent the difficult optimization problem often embedded in region characterization problems, and it also leads us to focus on the critical conditions in the outer bounds that make the inequalities become equalities, which effectively decouple the overall problem into several simpler sub-problems. Optimality results previously unknown in the literature are obtained using this novel approach. As a byproduct of the investigation, novel outer bounds are derived for these two problems.

On Joint Source-Channel Coding for a Multivariate Gaussian on a Gaussian MAC

In this paper, nonlinear distributed joint source-channel coding (JSCC) schemes for transmission of multivariate Gaussian sources over a Gaussian multiple access channel are proposed and analyzed. The main contribution is a zero-delay JSCC named Distributed Quantizer Linear Coder (DQLC), which performs relatively close the information theoretical bounds, improves when the correlation among the sources increases, and does not level off as the signal-to-noise ratio (SNR) becomes large. Therefore it outperforms any linear solution for sufficiently large SNR. Further an extension of DQLC to an arbitrary code length named Vector Quantizer Linear Coder (VQLC) is analyzed. The VQLC closes in on the performance upper bound as the code length increases and can potentially achieve the bound for any number of independent sources. The VQLC leaves a gap to the bound whenever the sources are correlated, however. JSCC achieving the bound for arbitrary correlation has been found for the bivariate case, but that solution is significantly outperformed by the DQLC/VQLC when there is a low delay constraint. This indicates that different approaches are needed to perform close to the bounds when the code length is high and low. The VQLC/DQLC also apply for bandwidth compression of a multivariate Gaussian transmitted on point-to-point links.

MAC With Action-Dependent State Information at One Encoder

The growing interest in action-dependent channels motivates us to extend the study of action-dependent settings, which until now focused on point-to-point models, to multiple-access channels (MACs). In this paper, we consider a two-user, state-dependent MAC, in which one of the encoders, called the informed (cognitive) encoder, is allowed to take an action that affects the formation of the channel states. Two independent messages are to be sent through the channel: (1) a common message known to both encoders and (2) a private message known only to the informed encoder. In addition, the informed encoder has access to the sequence of channel states in a noncausal manner. Our framework generalizes the previously evaluated settings of state-dependent point-to-point channels with actions and MACs with common messages. We derive a single letter characterization of the capacity region for this setting. Using this general result, we obtain and compute the capacity region for the Gaussian action-dependent MAC. The special methods used in solving the Gaussian case are then applied to obtain the capacity of the Gaussian action-dependent point-to-point channel, a problem left open and solved now. Finally, we establish some dualities between action-dependent channel coding and source coding problems. In particular, we obtain a duality equivalence between the considered MAC setting and the rate distortion model known as successive refinement with actions. This is done by developing a set of simple duality principles that enables us to successfully evaluate the outcome of one problem given the outcome of the other.

Secure Compute-and-Forward in a Bidirectional Relay

We consider the basic bidirectional relaying problem, in which two users in a wireless network wish to exchange messages through an intermediate relay node. In the compute-and-forward strategy, the relay computes a function of the two messages using the naturally occurring sum of symbols simultaneously transmitted by user nodes in a Gaussian multiple-access channel (MAC), and the computed function value is forwarded to the user nodes in an ensuing broadcast phase. In this paper, we study the problem under an additional security constraint, which requires that each user's message be kept secure from the relay. We consider two types of security constraints: 1) perfect secrecy, in which the MAC channel output seen by the relay is independent of each user's message and 2) strong secrecy, which is a form of asymptotic independence. We propose a coding scheme based on nested lattices, the main feature of which is that given a pair of nested lattices that satisfy certain goodness properties, we can explicitly specify probability distributions for randomization at the encoders to achieve the desired security criteria. In particular, our coding scheme guarantees perfect or strong secrecy even in the absence of channel noise. The noise in the channel only affects reliability of computation at the relay, and for Gaussian noise, we derive achievable rates for reliable and secure computation. We also present an application of our methods to the multihop line network in which a source needs to transmit messages to a destination through a series of intermediate relays.

Capacity-Achieving Distributions in Gaussian Multiple Access Channel With Peak Power Constraints

This paper addresses a two-user Gaussian multiple access channel (MAC) under peak power constraints at the transmitters. It is shown that generating the code-books of both users according to discrete distributions with a finite number of mass points achieves the largest weighted sum-rate in the network. This verifies that any point on the boundary of the capacity region of a two-user MAC under peak power constraints at both transmitters is achieved by discrete distributions with a finite number of mass points. Although the capacity-achieving distributions are not necessarily unique, it is verified that only discrete distributions with a finite number of mass points can achieve a point on the boundary of the capacity region. It is shown that there exist an infinite number of sum-rate-optimal points on the boundary of the capacity region. In contrast to the Gaussian MAC with average power constraints, we verify that time division (TD) cannot achieve any of the sum-rate-optimal points in the Gaussian MAC with peak power constraints. Using the so-called I-MMSE identity of Guo et al., the largest achievable sum-rate by orthogonal code division (OCD) is characterized where it is shown that Walsh-Hadamard spreading codes of length 2 are optimal. In the symmetric case where the peak power constraints at both transmitters are identical, we verify that OCD can achieve a sum-rate that is strictly larger than the highest sum-rate achieved by TD. Finally, it is demonstrated that there are values for the maximum peak power at the transmitters such that OCD can not achieve any of the sum-rate-optimal points on the boundary of the capacity region.

Short Length Trellis-Based Codes for Gaussian Multiple-Access Channels

We focus on trellis-based joint code design for two-user Gaussian multiple-access channel (MAC) in the short block length regime. We propose a design methodology, provide specific code designs and report numerical performance results. We compare the performance of the jointly designed codes with the performance of the codes designed for point-to-point (P2P) channels including optimum (in terms of minimum distance) convolutional codes. Our results show that the proposed codes achieve superior performance compared to these alternatives especially in the high signal-to-noise (SNR) regime in equal power scenarios.

Distributed Estimation and Detection With Bounded Transmissions Over Gaussian Multiple Access Channels

A distributed inference scheme which uses bounded transmission functions over a Gaussian multiple access channel is considered. When the sensor measurements are decreasingly reliable as a function of the sensor index, the conditions on the transmission functions under which consistent estimation and reliable detection are possible is characterized. For the distributed estimation problem, an estimation scheme that uses bounded transmission functions is proved to be strongly consistent provided that the variances of the noise samples are bounded and that the transmission function is one-to-one. The proposed estimation scheme is compared with the amplify-and-forward technique and its robustness to impulsive sensing noise distributions is highlighted. In contrast to amplify-and-forward schemes, it is also shown that bounded transmissions suffer from inconsistent estimates if the sensing noise variance goes to infinity. For the distributed detection problem, similar results are obtained by studying the deflection coefficient. Simulations corroborate our analytical results.

Energy‐efficiency region for multiple access channels

To investigate the trade-off between energy efficiency (EE) and spectral efficiency (SE) for Gaussian multiple access channels (MACs), a novel concept of the EE region is developed. The EE region for the time division multiple access system is also derived and compared. The SE–EE trade-off order is introduced to explicitly describe how fast the EE decays with SE in the high SE region. For a symmetric MAC, a constraint on SE–EE trade-off orders is derived and the Pareto optimum can be achieved by the corner points on the EE region.

The Approximate Sum Capacity of the Symmetric Gaussian &lt;inline-formula&gt; &lt;tex-math notation="TeX"&gt;$K$ &lt;/tex-math&gt;&lt;/inline-formula&gt;-User Interference Channel

Interference alignment has emerged as a powerful tool in the analysis of multiuser networks. Despite considerable recent progress, the capacity region of the Gaussian $K$ -user interference channel is still unknown in general, in part due to the challenges associated with alignment on the signal scale using lattice codes. This paper develops a new framework for lattice interference alignment, based on the compute-and-forward approach. Within this framework, each receiver decodes by first recovering two or more linear combinations of the transmitted codewords with integer-valued coefficients and then solving these linear combinations for its desired codeword. For the special case of symmetric channel gains, this framework is used to derive the approximate sum capacity of the Gaussian interference channel, up to an explicitly defined outage set of the channel gains. The key contributions are the capacity lower bounds for the weak through strong interference regimes, where each receiver should jointly decode its own codeword along with part of the interfering codewords. As part of the analysis, it is shown that decoding $K$ linear combinations of the codewords can approach the sum capacity of the $K$ -user Gaussian multiple-access channel up to a gap of no more than ${K}/{2}\log{K}$ bits.

A Closed-Form Solution to Implement Interference Alignment and Cancellation for a Gaussian Interference Multiple Access Channel

For interference alignment (IA) with no channel extension, determining the existence of IA solution for general system parameters is still an open problem. This same problem also exists in interference alignment and cancellation (IAC), which combines IA with interference cancellation in the receivers, involving a new receiver architecture associated with signaling over backhaul links among them. As IAC is expected to achieve more degrees of freedom (DoF) than IA, the existence of IAC solution would be another interesting, yet challenging issue to investigate. In this paper, we have proposed a specific alignment scheme, which allows for the derivation of closed-form IAC solution. Furthermore, we establish and prove the general necessary and sufficient condition to determine the existence of closed-form IAC solution for a Gaussian interference multiple access channel (MAC) with K receivers and J users, each with M antennas.

Distributed joint source-channel code design for GMAC using irregular LDPC codes

Separate source and channel coding is known to be sub-optimal for communicating correlated sources over a Gaussian multiple access channel (GMAC). This paper presents an approach to designing distributed joint source-channel (DJSC) codes for encoding correlated binary sources over a two-user GMAC, using systematic irregular low-density parity check (LDPC) codes. The degree profile defining the LDPC code is optimized for the joint source probabilities using extrinsic information transfer (EXIT) analysis and linear programming. A key issue addressed is the Gaussian modeling of log-likelihood ratios (LLRs) generated by nodes representing the joint source probabilities in the combined factor graph of the two LDPC codes, referred to as source-channel factor (SCF) nodes. It is shown that the analytical expressions based on additive combining of incoming LLRs, as done in variable nodes and parity check nodes of the graph of a single LDPC code, cannot be used with SCF nodes. To this end, we propose a numerical approach based on Monte-Carlo simulations to fit a Gaussian density to outgoing LLRs from the SCF nodes, which makes the EXIT analysis of the joint decoder tractable. Experimental results are presented which show that LDPC codes designed with the proposed approach outperforms previously reported DJSC codes for GMAC. Furthermore, they demonstrate that when the sources are strongly dependent, the proposed DJSC codes can achieve code rates higher than the theoretical upper-bound for separate source and channel coding.

Rematch-and-Forward: Joint Source–Channel Coding for Parallel Relaying With Spectral Mismatch

The Gaussian parallel relay network, introduced by Schein and Gallager, consists of a concatenation of a Gaussian additive broadcast channel from a single encoder to a layer of relays followed by a Gaussian multiple-access channel from the relays to the final destination (decoder), where all noises are independent. This setup exhibits an inherent conflict between digital and analog relaying; while analog relaying [known as amplify-and-forward (AF however, it is limited to white channels of equal bandwidth. In this paper, we present a generalization of the analog approach to the case of bandwidth mismatch. Our strategy, coined rematch and forward (R&F), is based upon applying joint source-channel coding techniques that belong to a certain class of maximally analog schemes. Using such techniques, R&F converts the bandwidth of the broadcast section to that of the multiple-access section, creating an equivalent matched-bandwidth network over which A&F is applied. It is shown that this strategy exploits the full bandwidth of the individual channels, without sacrificing the coherence gain offered by A&F. Specifically, for given individual-link capacities, R&F remains within a constant gap from the network capacity for any number of relays and any bandwidth ratio between the sections. Finally, the approach is extended to the case of colored channels.