Two-user Multiple Access Channel Research Articles

RIS-Aided Communications Over Dirty MAC: Capacity Region and Outage Probability

We characterize the capacity region of a two-user multiple access channel (MAC) in a reconfigurable intelligent surface (RIS)-aided communication system with side information (SI) at the transmitters. We consider two uplink communication scenarios: (i) a double dirty MAC where the interferences are known non-causally to both users; and (ii) a single dirty MAC model where only one of the users knows the interference. Considering that each of the users is assisted by a different RIS with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M_i</i> elements, we derive closed-form expressions for the capacity region and the outage probability (OP) for both system models. Results show that the use of RISs is beneficial to extend the capacity region and improve the OP in both scenarios.

Multiple Access Channel Simulation

We study the problem of simulating a two-user multiple-access channel (MAC) over a multiple access network of noiseless links. Two encoders observe independent and identically distributed (i.i.d.) copies of a source random variable each, while a decoder observes i.i.d. copies of a side-information random variable. There are rate-limited noiseless communication links between each encoder and the decoder, and there is independent pairwise shared randomness between all the three possible pairs of nodes. The decoder has to output approximately i.i.d. copies of another random variable jointly distributed with the two sources and the side information. We are interested in the rate tuples which permit this simulation. This setting can be thought of as a multi-terminal generalization of the point-to-point channel simulation problem studied by Bennett et al. (2002) and Cuff (2013). When the pairwise shared randomness between the encoders is absent, the setting reduces to a special case of MAC simulation using another MAC studied by Haddadpour et al. (2013). We establish that the presence of encoder shared randomness can strictly improve the communication rate requirements. We first show that the inner bound derived from Haddadpour et al. (2013) is tight when the sources at the encoders are conditionally independent given the side-information at the decoder. This result recovers the existing results on point-to-point channel simulation and function computation over such multi-terminal networks. We then explicitly compute the communication rate regions for an example both with and without the encoder shared randomness and demonstrate that its presence strictly reduces the communication rates. Inner and outer bounds for the general case are also obtained.

On the Age of Information in a Two-User Multiple Access Setup.

This work considers a two-user multiple access channel in which both users have Age of Information (AoI)-oriented traffic with different characteristics. More specifically, the first user has external traffic and cannot control the generation of status updates, and the second user monitors a sensor and transmits status updates to the receiver according to a generate-at-will policy. The receiver is equipped with multiple antennas and the transmitters have single antennas; the channels are subject to Rayleigh fading and path loss. We analyze the average AoI of the first user for a discrete-time first-come-first-served (FCFS) queue, last-come-first-served (LCFS) queue, and queue with packet replacement. We derive the AoI distribution and the average AoI of the second user for a threshold policy. Then, we formulate an optimization problem to minimize the average AoI of the first user for the FCFS and LCFS with preemption queue discipline to maintain the average AoI of the second user below a given level. The constraints of the optimization problem are shown to be convex. It is also shown that the objective function of the problem for the first-come-first-served queue policy is non-convex, and a suboptimal technique is introduced to effectively solve the problem using the algorithms developed for solving a convex optimization problem. Numerical results illustrate the performance of the considered optimization algorithm versus the different parameters of the system. Finally, we discuss how the analytical results of this work can be extended to capture larger setups with more than two users.

Broadcast Approach to Multiple Access With Local CSIT

A two-user multiple access channel is considered, in which the channels undergo slow block fading and the state of each channel is known only to its corresponding transmitter. This paper proposes a novel broadcast strategy for multiple access communication in this channel. In the broadcast approach, in principle, a transmitter with CSI uncertainty sends multiple independent superimposed information layers where the rate of each layer is adapted to a specific channel realization. In the existing broadcast approaches to multiuser communication, the transmitters often directly adopt a single-user strategy and each transmitter adapts its transmission to one unknown channel. The novel aspect of the proposed strategy is that it adapts the designed codebooks to the state of the entire network. This is motivated by the fact that the contribution of each user to the network-wide measures (e.g., capacity region) depends not only on the user’s direct channel to the receiver, but also on the qualities of other channels. Average achievable rate region and outer bounds on the capacity region are characterized. Furthermore, the expected capacity region is investigated, where most part of the capacity region boundary is characterized. Finally, an asymptotic capacity region is also characterized.

Uplink Non-Orthogonal Multiple Access With Finite-Alphabet Inputs

This paper focuses on the non-orthogonal multiple access (NOMA) design for a classical two-user multiple access channel (MAC) with finite-alphabet inputs. In contrast to most of the existing NOMA designs using continuous Gaussian input distributions, we consider practical quadrature amplitude modulation (QAM) constellations at both transmitters, the sizes of which are assumed to be not necessarily identical. We propose maximizing the minimum Euclidean distance of the received sum constellation with a maximum likelihood (ML) detector by adjusting the scaling factors (i.e., instantaneous transmitted powers and phases) of both users. The formulated problem is a mixed continuous–discrete optimization problem, which is nontrivial to resolve in general. By carefully observing the structure of the objective function, we define a new type of Farey sequence, termed punched Farey sequence to tackle the formulated problem. Based on this, we manage to achieve a closed-form optimal solution to the original problem by first dividing the entire feasible region into a finite number of Farey intervals and then taking the maximum over all possible intervals. The resulting sum constellation is proved to be a regular QAM constellation of a larger size, and hence, a simple quantization receiver can be implemented as the ML detector for the demodulation. Moreover, the superiority of NOMA over time-division multiple access in terms of minimum Euclidean distance is rigorously proved. We subsequently address how to extend our design framework intended for the two-user MAC to systems with multiple users and multiple antennas. Finally, simulation results are provided to verify our theoretical analysis and demonstrate the merits of the proposed NOMA over existing orthogonal and non-orthogonal designs.

Energy Harvesting Multiple Access Channels: Optimal and Near-Optimal Online Policies

We consider online transmission policies for a two-user multiple access channel, where both users harvest energy from nature. The energy harvests are independent and identically distributed (i.i.d.) over time, but can be arbitrarily correlated between the two users. The transmitters are equipped with arbitrary but finite-sized batteries. We focus on the online case where the transmitters know the energy arrivals only causally as they happen. The users do not know the probability distribution of the energy arrivals; each user knows only its own average recharge rate. We consider the most general case of arbitrarily distributed energy arrivals with arbitrary correlation between the users. In order to study this general case, we first study a special case for the energy arrivals, namely, we first consider the special case of synchronized (i.e., fully-correlated) Bernoulli energy arrivals at the two users. Even though the energy arrivals are fully-correlated, average recharge rates at the users are different due to the different battery sizes. For this case, we determine the exactly optimal policies that achieve the boundary of the long-term average capacity region. We show that the optimal power allocation policy is decreasing within the renewal interval, and that the long-term average capacity region is a single pentagon. We then propose a distributed fractional power (DFP) policy, which users implement distributedly with no knowledge of the other user’s energy arrival or battery state. We develop a lower bound on the performance of the DFP for synchronized Bernoulli energy arrivals. We then consider the case of two arbitrarily correlated asynchronous Bernoulli energy arrivals under the assumption of equal normalized average recharge rates. We show that extreme correlation between the energy sources hurts the achievable rate by showing that the throughput with asynchronous Bernoulli energy arrivals is larger than the throughput with the corresponding perfectly synchronized Bernoulli energy arrivals. We then show that under the DFP policy, the performance of Bernoulli energy arrivals forms a lower bound on the performance of any arbitrary energy arrivals. We also develop a universal upper bound on the performance of all online policies, and show that the proposed DFP is near-optimal in that it yields rates which are within a constant gap of the derived lower and upper bounds, and hence, of the optimal policy, for all system parameters.

Optimisation design of systematic LT codes over AWGN multiple access channel

Systematic Luby transform (SLT) codes over the additive white Gaussian noise (AWGN) multiple access channels (MACs) are analysed in this study. The authors introduce a novel optimisation model extending from the point-to-point AWGN channels to design the degree distributions over the AWGN MACs, which dramatically improve the bit-error-rate (BER) performance of SLT codes. First, they extend the Gaussian approximation analysis of SLT codes to the AWGN MACs to analyse the asymptotic BER performance where the symmetric condition of log-likelihood ratio message can no longer be assumed. Second, based on the asymptotic BER analysis over the AWGN MACs, they extend the existing optimisation model from the point-to-point AWGN channels to the AWGN MACs. Simulation results show that the degree distributions obtained in this study outperform other common degree distributions (optimised for single-user AWGN channels) over the two-user AWGN MACs.

Can Negligible Rate Increase Network Reliability?

In network cooperation strategies, nodes work together with the aim of increasing transmission rates or reliability. This paper demonstrates that enabling cooperation between the transmitters of a two-user multiple access channel via a cooperation facilitator that has access to both messages results in a network whose maximal- and average-error capacity regions are the same; this benefit ensues even when the information received by each transmitter is negligible. From this result, it follows that if a multiple access channel with no transmitter cooperation has different maximal- and average-error sum-capacities, then the maximal-error sum-capacity of the network consisting of this channel and a cooperation facilitator is not continuous with respect to the output edge capacities of the facilitator. Thus, there exist networks where adding negligible rate yields a non-negligible benefit.

Achievable Throughput of Energy Harvesting Fading Multiple-Access Channels Under Statistical QoS Constraints

This paper studies the achievable throughput of fading multiple-access channels (MACs) with energy harvesting transmitters subject to statistical quality of service (QoS) constraints in the form of limitations on the buffer overflow probability. Effective capacity, which characterizes the maximum constant arrival rate that a given process can support while satisfying the QoS constraints, is employed as the performance metric. Perfect channel state information (CSI) and energy arrivals are assumed to be available at both the transmitters and the receiver. With the assumption of naive power control scheme, in which the transmission power level is irrespective of the CSI and decided by the instantaneous harvested energy, the effective throughput regions of time division multiple access and superposition coding (SC) with fixed decoding are characterized. In the special case of the same QoS constraints, the optimal decoding order strategy for SC with variable decoding order is obtained. With the assumption that the channel states and harvested energy in all time slots are known at the transmitters, the point-to-point link is first revisited. Then, for a given decoding order strategy in two-user MACs, a suboptimal power control policy based on the average energy arrivals and causal energy and channel information is proposed and shown to achieve performance close to the optimal one.

LLR-Based SC Decoding of Polar Codes for Two-User Binary-Input MAC

This letter considers a hardware-friendly log-likelihood ratio (LLR)-based successive cancellation (SC) decoding of polar codes for two-user binary-input multiple access channels. Based on the known recursive equations in the likelihood domain, we obtain LLR-based recursive equations for the SC decoding. An approximate LLR-based decoding is also introduced, which shows small performance loss at high error rate, but has significantly low complexity compared with the previous likelihood-based decoding.

Cognition and Cooperation in Interfered Multiple Access Channels

In this work, we investigate a three-user cognitive communication network where a primary two-user multiple access channel suffers interference from a secondary point-to-point channel, sharing the same medium. While the point-to-point channel transmitter—transmitter 3—causes an interference at the primary multiple access channel receiver, we assume that the primary channel transmitters—transmitters 1 and 2—do not cause any interference at the point-to-point receiver. It is assumed that one of the multiple access channel transmitters has cognitive capabilities and cribs causally from the other multiple access channel transmitter. Furthermore, we assume that the cognitive transmitter knows the message of transmitter 3 in a non-causal manner, thus introducing the three-user multiple access cognitive Z-interference channel. We obtain inner and outer bounds on the capacity region of the this channel for both causal and strictly causal cribbing cognitive encoders. We further investigate different variations and aspects of the channel, referring to some previously studied cases. Attempting to better characterize the capacity region we look at the vertex points of the capacity region where each one of the transmitters tries to achieve its maximal rate. Moreover, we find the capacity region of a special case of a certain kind of more-capable multiple access cognitive Z-interference channels. In addition, we study the case of full unidirectional cooperation between the 2 multiple access channel encoders. Finally, since direct cribbing allows us full cognition in the case of continuous input alphabets, we study the case of partial cribbing, i.e., when the cribbing is performed via a deterministic function.

Gaussian Multiple Access via Compute-and-Forward

Lattice codes used under the Compute-and-Forward paradigm suggest an alternative strategy for the standard Gaussian multiple-access channel (MAC): The receiver successively decodes integer linear combinations of the messages until it can invert and recover all messages. In this paper, a multiple-access technique called CFMA (Compute-Forward Multiple Access) is proposed and analyzed. For the two-user MAC, it is shown that without time-sharing, the entire capacity region can be attained using CFMA with a single-user decoder as soon as the signal-to-noise ratios are above $1+\sqrt{2}$. A partial analysis is given for more than two users. Lastly the strategy is extended to the so-called dirty MAC where two interfering signals are known non-causally to the two transmitters in a distributed fashion. Our scheme extends the previously known results and gives new achievable rate regions.

Capacity Characterization for State-Dependent Gaussian Channel With a Helper

The state-dependent point-to-point Gaussian channel with a helper is first studied, in which a transmitter communicates with a receiver via a state-corrupted channel. The state is not known to the transmitter nor to the receiver, but known to a helper noncausally, which then wishes to assist the receiver to cancel the state. Differently from the previous work that characterized the capacity only in the infinite state power regime, this paper explores the general case with arbitrary state power. A lower bound on the capacity is derived based on an achievable scheme that integrates direct state subtraction and single-bin dirty paper coding. By analyzing this lower bound and further comparing it with the existing upper bounds, the capacity of the channel is characterized for a wide range of channel parameters. Such an idea of characterizing the capacity is further extended to study the two-user state-dependent multiple access channel with a helper. By comparing the derived inner and outer bounds, the channel parameters are partitioned into appropriate cases, and for each case, either segments on the capacity region boundary or the full capacity region are characterized.

Performance of Multilevel Flash Memories With Different Binary Labelings: A Multi-User Perspective

In this paper, we study the performance of different decoding schemes for multilevel flash memories where each page in every block is encoded independently. We focus on multi-level cell flash memory, which is modeled as a two-user multiple-access channel suffering from asymmetric noise. The uniform rate regions and sum rates of treating interference as noise decoding and successive cancelation decoding are investigated for a program/erase cycling model and a data retention model. We examine the effect of different binary labelings of the cell levels, as well as the impact of further quantization of the memory output (i.e., additional read thresholds). Finally, we extend our analysis to the three-level cell flash memory.

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.

Multiple Access Channels With States Causally Known at Transmitters

It has been recently shown by Lapidoth and Steinberg that strictly causal state information can be beneficial in multiple access channels (MACs). Specifically, it was proved that the capacity region of a two-user MAC with independent states, each known strictly causally to one encoder, can be enlarged by letting the encoders send compressed past state information to the decoder. In this work, a generalization of the said strategy is proposed whereby the encoders compress also the past transmitted codewords along with the past state sequences. The proposed scheme uses a combination of long-message encoding, compression of the past state sequences and codewords without binning, and joint decoding over all transmission blocks. The proposed strategy has been recently shown by Lapidoth and Steinberg to strictly improve upon the original one. Capacity results are then derived for a class of channels that include two-user modulo-additive state-dependent MACs. Moreover, the proposed scheme is extended to state-dependent MACs with an arbitrary number of users. Finally, output feedback is introduced and an example is provided to illustrate the interplay between feedback and availability of strictly causal state information in enlarging the capacity region.

Differential Coding for MAC Based Two-User MIMO Communication Systems

In this paper, we explain how to implement differential modulation in multiple access channel (MAC) based uplink two-user multiple-input multiple-output (MIMO) communication system. It is assumed that the users cannot exchange their information and transmit data over uplink MAC channels simultaneously in the same frequency band and without any orthogonal signatures (no CDMA). We derive two types of differential decoders for two-user MIMO MAC system namely 1) Partial differential decoder, 2) Heuristic based differential decoders. The partial differential decoder is able to avoid the knowledge of the channel gains of one user at the receiver for joint decoding of the data of both users. Whereas, the heuristic differential decoders are obtained heuristically and work without any channel knowledge of both users. For the heuristic differential decoder to work properly, the data of one user must be rotated before transmission. An upper bound of the pairwise error probability (PEP) is derived for the proposed scheme. The upper bound of the PEP is minimized for obtaining an optimized value of the rotation angle.

Polar Codes for the Two-User Multiple-Access Channel

Arikan's polar coding method is extended to two-user multiple-access channels. It is shown that if the two users of the channel use the Arikan construction, the resulting channels will polarize to one of five possible extremals, on each of which uncoded transmission is optimal. The sum rate achieved by this coding technique is the one that correponds to uniform input distributions. The encoding and decoding complexities and the error performance of these codes are as in the single-user case: $O(n\log n)$ for encoding and decoding, and $o(\exp(-n^{1/2-\epsilon}))$ for block error probability, where $n$ is the block length.

New Space–Time Code Constructions for Two-User Multiple Access Channels

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper addresses the problem of constructing multiuser multiple-input multiple-output (MU-MIMO) codes for two users. The users are assumed to be equipped with <formula formulatype="inline"><tex Notation="TeX">$n_{t}$</tex> </formula> transmit antennas, and there are <formula formulatype="inline"> <tex Notation="TeX">$n_{r}$</tex></formula> antennas available at the receiving end. A general scheme is proposed and shown to achieve the optimal diversity-multiplexing gain tradeoff (DMT). Moreover, an explicit construction for the special case of <formula formulatype="inline"><tex Notation="TeX">$n_{t}=2$</tex></formula> and <formula formulatype="inline"><tex Notation="TeX">$n_{r}=2$</tex></formula> is given, based on the optimization of the code shape and density. All the proposed constructions are based on cyclic division algebras and their orders and take advantage of the multi-block structure. Computer simulations show that both the proposed schemes yield codes with excellent performance improving upon the best previously known codes. Finally, it is shown that the previously proposed design criteria for DMT optimal MU-MIMO codes are sufficient but in general too strict and impossible to fulfill. Relaxed alternative design criteria are then proposed and shown to be still sufficient for achieving the multiple-access channel diversity-multiplexing tradeoff. </para>

An achievable rate region of cooperative multiple-access channels with hybrid CF and DF cooperation

In this letter, we derive an achievable rate region of a two-user cooperative multiple-access (CMA) channel where one user performs decode-and-forward (DF) cooperation and the other user performs Wyner-Ziv-type compress-and-forward (CF) cooperation. The proposed rate region is achieved using a communication scheme that applies block Markov coding at each user and backward decoding at destination. Numerical results show that for some channel scenarios, the proposed hybrid CF and DF cooperation scheme enlarges the rate region achieved by the pure DF-based cooperation scheme.