Gaussian Multiple Access Channel Research Articles

Rate-Diverse Multiple Access Over Gaussian Channels

In this work, we develop a pair of rate-diverse encoder and decoder for a two-user Gaussian multiple access channel (GMAC). The proposed scheme enables the users to transmit with the same codeword length but different coding rates under diverse user channel conditions. First, we propose the row-combining (RC) method and row-extending (RE) method to design practical low-density parity-check (LDPC) channel codes for rate-diverse GMAC. Second, we develop an iterative rate-diverse joint user messages decoding (RDJD) algorithm for GMAC, where all user messages are decoded with a single parity-check matrix. In contrast to the conventional network-coded multiple access (NCMA) and compute-forward multiple access (CFMA) schemes that first recover a linear combination of the transmitted codewords and then decode both user messages, this work can decode both the user messages simultaneously. Extrinsic information transfer (EXIT) chart analysis and simulation results indicate that RDJD can achieve gains up to 1.0 dB over NCMA and CFMA in the two-user GMAC. In particular, we show that there exists an optimal rate allocation for the two users to achieve the best decoding performance given the channel conditions and sum rate.

Unsourced Multiple Access With Random User Activity

To account for the massive uncoordinated random access scenario, which is relevant for the Internet of Things, Polyanskiy (2017) proposed a novel formulation of the multiple-access problem, commonly referred to as unsourced multiple access, where all users employ a common codebook and the receiver decodes up to a permutation of the messages. In this paper, we extend this seminal work to the case where the number of active users is random and unknown <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> . We define a random-access code accounting for both misdetection (MD) and false alarm (FA), and derive a random-coding achievability bound for the Gaussian multiple access channel. Our bound captures the fundamental trade-off between MD and FA probabilities. It suggests that the lack of knowledge of the number of active users entails a small penalty in energy efficiency when the target MD and FA probabilities are high. However, as the target MD and FA probabilities decrease, the energy efficiency penalty becomes more significant. For example, in a typical IoT scenario with framelength 19200 complex channel uses and 25–300 active users in average, the required energy per bit to achieve both MD and FA probabilities below 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> , predicted by our bound, is only 0.5–0.7 dB higher than that predicted by the bound in Polyanskiy (2017) for a known number of active users. This gap increases to 3–4 dB when the target MD probability and/or FA probability is below 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . Taking both MD and FA into account, we use our bound to benchmark the energy efficiency of slotted-ALOHA with multi-packet reception, of a decoder that simply treats interference as noise, and of some recently proposed unsourced multiple access schemes. Numerical results suggest that, when the target MD and FA probabilities are high, it is effective to estimate the number of active users, then treat this estimate as the true value, and use a coding scheme that performs well for the case of known number of active users. However, this approach becomes energy inefficient when the requirements on MD and FA probabilities are stringent.

Non-Orthogonal Multiple Access with One-Bit Analog-to-Digital Converters Using Threshold Adaptation.

In digital communication systems featuring high-resolution analog-to-digital converters (ADCs), the utilization of successive interference cancellation and detection can enhance the capacity of a Gaussian multiple access channel (MAC) by combining signals from multiple transmitters in a non-orthogonal manner. Conversely, in systems employing one-bit ADCs, it is exceedingly difficult to eliminate non-orthogonal interference using digital signal processing due to the considerable distortion present in the received signal when employing such ADCs. As a result, the Gaussian MAC does not yield significant capacity gains in such cases. To address this issue, we demonstrate that, under a given deterministic interference, the capacity of a one-bit-quantized channel becomes equivalent to the capacity without interference when an appropriate threshold value is chosen. This finding suggests the potential for indirect interference cancellation in the analog domain, facilitating the proposition of an efficient successive interference cancellation and detection scheme. We analyze the achievable rate of the proposed scheme by deriving the mutual information between the transmitted and received signals at each detection stage. The obtained results indicate that the sum rate of the proposed scheme generally outperforms conventional methods, with the achievable upper bound being twice as high as that of the conventional methods. Additionally, we have developed an optimal transmit power allocation algorithm to maximize the sum rate in fading channels.

Efficient Massive Machine Type Communication (mMTC) via AMP

We propose efficient and low-complexity multiuser detection (MUD) algorithms for Gaussian multiple access channel (G-MAC) for short-packet transmission in massive machine type communications. To do so, we first formulate the G-MAC MUD problem as a sparse signal recovery problem and obtain the exact and approximate joint prior distribution of the sparse vector to be recovered. Then, we employ the Bayesian approximate message passing (AMP) algorithms with the optimal separable and nonseparable minimum mean squared error (MMSE) denoisers for soft decoding of the sparse vector. The effectiveness of the proposed MUD algorithms for a large number of devices is supported by simulation results. For packets of 8 information bits, while the state-of-the-art AMP with soft-threshold denoising achieves 8/100 of the upper bound at Eb/N0 = 4 dB, the proposed algorithms reach 4/7 and 1/2 of the upper bound.

Lossy State Communication over Fading Multiple Access Channels.

Joint communications and sensing functionalities integrated into the same communication network have become increasingly relevant due to the large bandwidth requirements of next-generation wireless communication systems and the impending spectral shortage. While there exist system-level guidelines and waveform design specifications for such systems, an information-theoretic analysis of the absolute performance capabilities of joint sensing and communication systems that take into account practical limitations such as fading has not been addressed in the literature. Motivated by this, we undertake a network information-theoretic analysis of a typical joint communications and sensing system in this paper. Towards this end, we consider a state-dependent fading Gaussian multiple access channel (GMAC) setup with an additive state. The state process is assumed to be independent and identically distributed (i.i.d.) Gaussian, and non-causally available to all the transmitting nodes. The fading gains on the respective links are assumed to be stationary and ergodic and available only at the receiver. In this setting, with no knowledge of fading gains at the transmitters, we are interested in joint message communication and estimation of the state at the receiver to meet a target distortion in the mean-squared error sense. Our main contribution here is a complete characterization of the distortion-rate trade-off region between the communication rates and the state estimation distortion for a two-sender GMAC. Our results show that the optimal strategy is based on static power allocation and involves uncoded transmissions to amplify the state, along with the superposition of the digital message streams using appropriate Gaussian codebooks and dirty paper coding (DPC). This acts as a design directive for realistic systems using joint sensing and transmission in next-generation wireless standards and points to the relative benefits of uncoded communications and joint source-channel coding in such systems.

Coded Over-the-Air Computation for Model Aggregation in Federated Learning

This letter introduces a new coded transmission design for model aggregation in federated learning (FL) over Gaussian multiple access channels (MAC), named coded over-the-air computation (codedAirComp). It enjoys the optimality of analog AirComp-based uncoded transmission for fast model aggregation, but also leverages the traditional source-channel separation principle for more practical uses. Specifically, the proposed codedAirComp employs stochastic uniform quantization for local gradient compression and nested lattice coding for channel transmission. Compared with the traditional coding scheme, the proposed scheme significantly reduces the model aggregation distortion and improves the overall learning accuracy.

Gaussian Multiuser Wiretap Channels in the Presence of a Jammer-Aided Eavesdropper.

This paper considers secure communication in the presence of an eavesdropper and a malicious jammer. The jammer is assumed to be oblivious of the communication signals emitted by the legitimate transmitter(s) but can employ any jamming strategy subject to a given power constraint and shares her jamming signal with the eavesdropper. Four such models are considered: (i) the Gaussian point-to-point wiretap channel; (ii) the Gaussian multiple-access wiretap channel; (iii) the Gaussian broadcast wiretap channel; and (iv) the Gaussian symmetric interference wiretap channel. The use of pre-shared randomness between the legitimate users is not allowed in our models. Inner and outer bounds are derived for these four models. For (i), the secrecy capacity is obtained. For (ii) and (iv) under a degraded setup, the optimal secrecy sum-rate is characterized. Finally, for (iii), ranges of model parameter values for which the inner and outer bounds coincide are identified.

Design of Protograph-Based LDPC Codes for Two-User Gaussian Multiple Access Channel

In this letter, we study the performance of protograph-based low-density parity-check (LDPC) codes for two-user Gaussian multiple access channel (GMAC). Considering the characteristic of a joint protograph of two users, we first derive a joint protograph-based extrinsic information transfer (JP-EXIT) chart to analyze the iterative user decoding behavior of two-user GMAC. Guided by the JP-EXIT, we further propose a new design scheme and construct protograph base matrices of different code rates for two users, respectively. Both theoretical analyses and simulation results show that the proposed protograph-based LDPC codes of low decoding threshold outperform the conventional irregular LDPC codes for both equal-power and unequal-power GMAC with different code rates.

Covert Communication Over Gaussian Multiple-Access Channels With Feedback

We consider the covert communication over the two-user Gaussian multiple access channel (GMAC) with causal feedback. It is shown that any causal feedback does not enlarge the covert capacity region and the time-division scheme is optimal for a class of channels, which includes the case where the warden observes what the legitimate receiver receives. For the proof, we derive an outer bound on the covert capacity region of general GMACs with noiseless causal feedback, which implies that the square-root law holds for arbitrary channel gains. Furthermore, the extension to multi-user case is presented.

Self-Secure Capacity-Achieving Feedback Schemes of Gaussian Multiple-Access Wiretap Channels With Degraded Message Sets

Self-Secure Capacity-Achieving Feedback Schemes of Gaussian Multiple-Access Wiretap Channels With Degraded Message Sets

Near-Optimal Coding for Many-User Multiple Access Channels

This paper considers the Gaussian multiple-access channel (MAC) in the asymptotic regime where the number of users grows linearly with the code length. We propose efficient coding schemes based on random linear models with approximate message passing (AMP) decoding and derive the asymptotic error rate achieved for a given user density, user payload (in bits), and user energy. The tradeoff between energy-per-bit and achievable user density (for a fixed user payload and target error rate) is studied, and it is demonstrated that in the large system limit, a spatially coupled coding scheme with AMP decoding achieves near-optimal tradeoffs for a wide range of user densities. Furthermore, in the regime where the user payload is large, we also study the tradeoff between energy-per-bit and spectral efficiency and discuss methods to reduce decoding complexity.

Computable limits of optical multiple-access communications

Communication rates over quantum channels can be boosted by entanglement, via superadditivity phenomena or entanglement assistance. Superadditivity refers to the capacity improvement from entangling inputs across multiple channel uses. Nevertheless, when unlimited entanglement assistance is available, the entanglement between channel uses becomes unnecessary -- the entanglement-assisted (EA) capacity of a single-sender and single-receiver channel is additive. We generalize the additivity of EA capacity to general multiple-access channels (MACs) for the total communication rate. Furthermore, for optical communication modelled as phase-insensitive bosonic Gaussian MACs, we prove that the optimal total rate is achieved by Gaussian entanglement and therefore can be efficiently evaluated. To benchmark entanglement's advantage, we propose computable outer bounds for the capacity region without entanglement assistance. Finally, we formulate an EA version of minimum entropy conjecture, which leads to the additivity of the capacity region of phase-insensitive bosonic Gaussian MACs if it is true. The computable limits confirm entanglement's boosts in optical multiple-access communications.

Over-the-Air Statistical Estimation

We study schemes and lower bounds for distributed minimax statistical estimation over a Gaussian multiple-access channel (MAC) under squared error loss. Our framework combines statistical estimation and wireless communication. First, we develop &#x201C;analog&#x201D; joint estimation-communication schemes that exploit the superposition property of the Gaussian MAC. We characterize their risk in terms of the number of nodes and dimension of the parameter space. Then, we derive information-theoretic lower bounds on the minimax risk of any estimation scheme that is restricted to communicate the samples over a given number of uses of the channel. This shows that the risk achieved by our proposed schemes is within a logarithmic factor of these lower bounds. We compare both achievability and lower bound results to previous &#x201C;digital&#x201D; lower bounds, where nodes transmit errorless bits at the Shannon capacity of the MAC. Our key finding is that analog estimation schemes that leverage the physical layer offer a drastic reduction in estimation error over digital schemes relying on a physical-layer abstraction.

Deep-learning-aided design of LDPC coding scheme for two-user Gaussian multiple access channels

Deep-learning-aided design of LDPC coding scheme for two-user Gaussian multiple access channels

Self-Secure Capacity-Achieving Feedback Schemes of Gaussian Multiple-Access Wiretap Channels With Degraded Message Sets

It has been shown that the SK scheme, which was proposed by Schalkwijk and Kailath, is a self-secure capacity-achieving (SSCA) feedback scheme for the Gaussian wiretap channel, i.e., the SK scheme not only achieves the feedback capacity of the Gaussian channel, but also is secure by itself and achieves the feedback secrecy capacity of the Gaussian wiretap channel. For the multi-user wiretap channels, very recently, it has been shown that Ozarow’s capacity-achieving feedback scheme for the two-user Gaussian multiple-access channel (GMAC) is the SSCA feedback scheme for the two-user Gaussian multiple-access wiretap channel (GMAC-WT). In this paper, first, we propose a SSCA feedback scheme for the two-user GMAC-WT with degraded message sets (GMAC-WT-DMS). Next, we extend the above scheme to the two-user GMAC-WT-DMS with noncausal channel state information at the transmitters (NCSIT), and show that the extended scheme is also a SSCA feedback scheme. Finally, we derive outer bounds on the secrecy capacity regions of the two-user GMAC-WT-DMS with or without NCSIT, and numerical results show the rate gains by the feedback.

Gaussian Multiple and Random Access Channels: Finite-Blocklength Analysis

This paper presents finite-blocklength achievability bounds for the Gaussian multiple access channel (MAC) and random access channel (RAC) under average-error and maximal-power constraints. Using random codewords uniformly distributed on a sphere and a maximum likelihood decoder, the derived MAC bound on each transmitter's rate matches the MolavianJazi-Laneman bound (2015) in its first- and second-order terms, improving the remaining terms to $\frac12\frac{\log n}{n}+O \left(\frac 1 n \right)$ bits per channel use. The result then extends to a RAC model in which neither the encoders nor the decoder knows which of $K$ possible transmitters are active. In the proposed rateless coding strategy, decoding occurs at a time $n_t$ that depends on the decoder's estimate $t$ of the number of active transmitters $k$. Single-bit feedback from the decoder to all encoders at each potential decoding time $n_i$, $i \leq t$, informs the encoders when to stop transmitting. For this RAC model, the proposed code achieves the same first-, second-, and third-order performance as the best known result for the Gaussian MAC in operation.

Uplink-Downlink Duality Between Multiple-Access and Broadcast Channels With Compressing Relays

Uplink-downlink duality refers to the fact that under a sum-power constraint, the capacity regions of a Gaussian multiple-access channel and a Gaussian broadcast channel with Hermitian transposed channel matrices are identical. This paper generalizes this result to a cooperative cellular network, in which remote access-points are deployed as relays in serving the users under the coordination of a central processor (CP). In this model, the users and the relays are connected over noisy wireless links, while the relays and the CP are connected over noiseless but rate-limited fronthaul links. Based on a Lagrangian technique, this paper establishes a duality relationship between such a multiple-access relay channel and broadcast relay channel, under the assumption that the relays use compression-based strategies. Specifically, we show that under the same total transmit power constraint and individual fronthaul rate constraints, the achievable rate regions of the Gaussian multiple-access and broadcast relay channels are identical, when either independent compression or Wyner-Ziv and multivariate compression strategies are used. The key observations are that if the beamforming vectors at the relays are fixed, the sum-power minimization problems under the achievable rate and fronthaul constraints in both the uplink and the downlink can be transformed into either a linear programming or a semidefinite programming problem depending on the compression technique, and that the uplink and downlink problems are Lagrangian duals of each other. Moreover, the dual variables corresponding to the downlink rate constraints become the uplink powers; the dual variables corresponding to the downlink fronthaul constraints become the uplink quantization noises. This duality relationship enables an efficient algorithm for optimizing the downlink transmission and relaying strategies based on the uplink.

On Error Exponents of Encoder-Assisted Communication Systems

We consider a point–to–point communication system, where in addition to the encoder and the decoder, there is a helper that observes non–causally the realization of the noise vector and provides a (lossy) rate– $ {R}_{{ \text { h}}}$ description of it to the encoder ( $ {R}_{{ \text { h}}} ). In continuation to Lapidoth and Marti (2020), who derived the capacity of this model, here our focus is on error exponents. We consider both continuous–alphabet, additive white Gaussian channels and finite–alphabet, modulo–additive channels, and for each one of them, we study the cases of both fixed–rate and variable–rate noise descriptions by the helper. Our main finding is that, as long as the channel–coding rate, R, is below the helper–rate, $ {R}_{{ \text { h}}}$ , the achievable error exponent is unlimited (i.e., it can be made arbitrarily large), and in some of the cases, it is even strictly infinite (i.e., the error probability can be made strictly zero). However, in the range of coding rates $( {R}_{{ \text { h}}}, {R}_{{ \text { h}}}+ {C}_{0})$ , C0 being the ordinary channel capacity (without help), the best achievable error exponent is finite and strictly positive, although there is a certain gap between our upper bound (converse bound) and lower bound (achievability) on the highest achievable error exponent. This means that the model of encoder–assisted communication is essentially equivalent to a model, where in addition to the noisy channel between the encoder and decoder, there is also a parallel noiseless bit–pipe of capacity $ {R}_{{ \text { h}}}$ . We also extend the scope to the Gaussian multiple access channel (MAC) and characterize the rate sub–region, where the achievable error exponent is unlimited or even infinite.

User-Load-Compatible Masking Schemes for Raptor-Like Protograph-Based LDPC Codes in Gaussian Multiple Access Channels

In this paper, the backward-compatible coding schemes are explored to achieve the near-capacity performances in dynamic LDPC-coded Gaussian multiple access channels (GMAC). Specifically, some user-load-compatible (ULC) masked edges in a raptor-like protograph are masked with the variation of user load u. To distinguish the edges in a protograph, a multi-user protograph-based extrinsic information transfer (MU-PEXIT) chart is developed. Based on this chart, an iterative edge selection algorithm combined with a theoretical simplification is proposed to facilitate the selection of independent masked edge sets (MESs) for varying u. To further decrease the complexity of the independent masking scheme, a nested version is presented, where the MESs for varying u are nested and derived from the same mother MES. Meanwhile, nested selection algorithms are provided to select the nested MESs. Extensive simulation results demonstrate that the masked 5G-NR LDPC codes can maintain near-capacity performances regardless of the variation of u. Besides, these ULC masked codes achieve comparable performances with the state-of-the-art LDPC codes which are specially re-designed in a static GMAC.

Cooperative Multiple-Access Channels With Distributed State Information

This paper studies a memoryless state-dependent multiple access channel (MAC) where two transmitters wish to convey a message to a receiver under the assumption of causal and imperfect channel state information at transmitters (CSIT) and imperfect channel state information at receiver (CSIR). In order to emphasize the limitation of transmitter cooperation between physically distributed nodes, we focus on the so-called distributed CSIT assumption, i.e., where each transmitter has its individual channel knowledge, while the message can be assumed to be partially or entirely shared a priori between transmitters by exploiting some on-board memory. Under this setup, the first part of the paper characterizes the common message capacity of the channel at hand for arbitrary CSIT and CSIR structure. The optimal scheme builds on Shannon strategies, i.e., optimal codes are constructed by letting the channel inputs be a function of current CSIT only. For a special case when CSIT is a deterministic function of CSIR, the considered scheme also achieves the capacity region of a common message and two private messages. The second part addresses an important instance of the previous general result in a context of a cooperative multi-antenna Gaussian channel under i.i.d. fading operating in frequency-division duplex mode, such that CSIT is acquired via an explicit feedback of perfect CSIR. The capacity of the channel at hand is achieved by distributed linear precoding applied to Gaussian codes. Surprisingly, we demonstrate that it is suboptimal to send a number of data streams bounded by the number of transmit antennas as typically considered in a centralized CSIT setup. Finally, numerical examples are provided to evaluate the sum capacity of the binary MAC with binary states as well as the Gaussian MAC with i.i.d. fading.