This paper considers the problem of distributed lossy compression where the goal is to recover one or more linear combinations of the sources at the decoder, subject to distortion constraints. For certain configurations, it is known that codes with algebraic structure can outperform i.i.d. codebooks. For the special case of finite-alphabet sources, recent work has demonstrated how to incorporate joint typicality decoding alongside linear encoding and binning. This work takes a discretization approach to extend this rate region to include both integer- and real-valued sources. As a case study, the rate region is evaluated for the Gaussian case. The resulting joint-typicality-based rate region recovers and generalizes the best-known rate region for this scenario, based on lattice encoding and sequential decoding.

Compute–forward is a coding technique that enables receiver(s) in a network to directly decode one or more linear combinations of the transmitted codewords. Initial efforts focused on Gaussian channels and derived achievable rate regions via nested lattice codes and single-user (lattice) decoding as well as sequential (lattice) decoding. Recently, these results have been generalized to discrete memoryless channels via nested linear codes and joint typicality coding, culminating in a simultaneous-decoding rate region for recovering one or more linear combinations from$K$users. Using a discretization approach, this paper translates this result into a simultaneous-decoding rate region for a wide class of continuous memoryless channels, including the important special case of Gaussian channels. Additionally, this paper derives a single, unified expression for both discrete and continuous rate regions via an algebraic generalization of Rényi’s information dimension.

Grant-free random access (RA) techniques are suitable for machine-type communication (MTC) networks but they need to be adaptive to the MTC traffic, which is different from the human-type communication. Conventional RA protocols such as exponential backoff (EB) schemes for slotted-ALOHA suffer from a high number of collisions and they are not directly applicable to the MTC traffic models. In this work, we propose to use multi-agent deep Q-network (DQN) with parameter sharing to find a single policy applied to all machine-type devices (MTDs) in the network to resolve collisions. Moreover, we consider binary broadcast feedback common to all devices to reduce signalling overhead. We compare the performance of our proposed DQN-RA scheme with EB schemes for up to 500 MTDs and show that the proposed scheme outperforms EB policies and provides a better balance between throughput, delay and collision rate.

Random access (RA) schemes are a topic of high interest in machine-type communication (MTC). In RA protocols, backoff techniques such as exponential backoff (EB) are used to stabilize the system to avoid low throughput and excessive delays. However, these backoff techniques show varying performance for different underlying assumptions and analytical models. Therefore, finding a better transmission policy for slotted ALOHA RA is still a challenge. In this paper, we show the potential of deep reinforcement learning (DRL) for RA. We learn a transmission policy that balances between throughput and fairness. The proposed algorithm learns transmission probabilities using previous action and binary feedback signal, and it is adaptive to different traffic arrival rates. Moreover, we propose average age of packet (AoP) as a metric to measure fairness among users. Our results show that the proposed policy outperforms the baseline EB transmission schemes in terms of throughput and fairness.

We present a novel unified framework of compute-forward achievable rate regions for simultaneous decoding of multiple linear codeword combinations. This framework covers a wide class of discrete and continuous-input channels, and computation over finite fields, integers, and reals. The resulting rate regions recover several well-known achievability results, and in some cases extend them. The framework is built upon a recently established achievable rate region based on linear codes and joint typicality decoding. The latter is extended from finite fields to computation over the integers and, via a discretization approach, to computation over the reals with integer coefficients and continuous inputs. Evaluating the latter with Gaussian distributions, we obtain a closed-form rate region which generalizes the classic compute-forward rates originally derived by means of lattice codes by Nazer and Gastpar.

We consider a setup in which confidential i.i.d. samples $X_1,\dotsc,X_n$ from an unknown finite-support distribution $\boldsymbol{p}$ are passed through $n$ copies of a discrete privatization channel (a.k.a. mechanism) producing outputs $Y_1,\dotsc,Y_n$. The channel law guarantees a local differential privacy of $\epsilon$. Subject to a prescribed privacy level $\epsilon$, the optimal channel should be designed such that an estimate of the source distribution based on the channel outputs $Y_1,\dotsc,Y_n$ converges as fast as possible to the exact value $\boldsymbol{p}$. For this purpose we study the convergence to zero of three distribution distance metrics: $f$-divergence, mean-squared error and total variation. We derive the respective normalized first-order terms of convergence (as $n \to \infty$), which for a given target privacy $\epsilon$ represent a rule-of-thumb factor by which the sample size must be augmented so as to achieve the same estimation accuracy as that of a non-randomizing channel. We formulate the privacy-fidelity trade-off problem as being that of minimizing said first-order term under a privacy constraint $\epsilon$. We further identify a scalar quantity that captures the essence of this trade-off, and prove bounds and data-processing inequalities on this quantity. For some specific instances of the privacy-fidelity trade-off problem, we derive inner and outer bounds on the optimal trade-off curve.

A novel coding strategy is proposed for a broadcast setting with two transmitter (TX) antennas and two single-antenna receivers (RX). The strategy consists of using space-time block coding to send a common message (to be decoded by both RXs) across the two TX antennas, while each TX antenna also sends a private message to one of the RXs. The relative weight of the private and common messages from each TX antenna is tuned to maximize the instantaneous achievable sum-rate of the channel. Closed-form expressions for the optimal weight factors are derived. In terms of the generalized degrees of freedom (GDoF) metric, the new scheme is able to achieve the sum-GDoF with finite precision channel state information at the transmitter (CSIT) of the two user broadcast channel. Moreover, as opposed to the existing rate-splitting schemes, the proposed scheme yields instantaneous achievable rates that are independent of the channel phases. This property is instrumental for link adaptation when only magnitude CSIT is available. Our numerical results indeed demonstrate the superiority of the scheme for the 2-user setting in case of magnitude CSIT. Extension to a more general K-user scenario is briefly discussed.

Non-Coherent Rate-Splitting (NCRS) was recently proposed as a practical multiuser coding and decoding scheme to increase the spectral efficiency of multibeam satellite communication systems. In this paper, we further study the practical realization of NCRS. We propose a modified coding scheme (NCRS*) that is robust to a nonzero time offset among beams. In NCRS*, as opposed to NCRS, the beams send independently channel encoded and modulated waveforms. We assess the performance of NCRS* in terms of the achievable rate region. It is shown that NCRS* performs worse than NCRS, but better than or comparable to other competing schemes, which, as opposed to NCRS*, require flexible bandwidth allocation or perfect synchronization at the transmitter. We also propose a new N-MAP algorithm for the practical implementation of NCRS* receivers. Similar to the existing UMAP algorithm, N-MAP takes into account the modulation used by, and the time offset between, the signals received from the different beams. In most cases, however, N-MAP has a significantly lower complexity than U-MAP.

Algebraic network information theory is an emerging facet of network information theory, studying the achievable rates of random code ensembles that have algebraic structure, such as random linear codes. A distinguishing feature is that linear combinations of codewords can sometimes be decoded more efficiently than codewords themselves. The present work further develops this framework by studying the simultaneous decoding of multiple messages. Specifically, consider a receiver in a multi-user network that wishes to decode several messages. Simultaneous joint typicality decoding is one of the most powerful techniques for determining the fundamental limits at which reliable decoding is possible. This technique has historically been used in conjunction with random i.i.d. codebooks to establish achievable rate regions for networks. Recently, it has been shown that, in certain scenarios, nested linear codebooks in conjunction with “single-user” or sequential decoding can yield better achievable rates. For instance, the compute-forward problem examines the scenario of recovering L ≤ K linear combinations of transmitted codewords over a K-user multiple-access channel (MAC), and it is well established that linear codebooks can yield higher rates. This paper develops bounds for simultaneous joint typicality decoding used in conjunction with nested linear codebooks, and applies them to obtain a larger achievable region for compute-forward over a K-user discrete memoryless MAC. The key technical challenge is that competing codeword tuples that are linearly dependent on the true codeword tuple introduce statistical dependencies, which requires careful partitioning of the associated error events.

Consider the important special case of the K-user distributed source coding problem where the decoder only wishes to recover one or more linear combinations of the sources. The work of Körner and Marton demonstrated that, in some cases, the optimal rate region is attained by random linear codes, and strictly improves upon the best-known achievable rate region established via random i.i.d. codes. Recent efforts have sought to develop a framework for characterizing the achievable rate region for nested linear codes via joint typicality encoding and decoding. Here, we make further progress along this direction by proposing an achievable rate region for simultaneous joint typicality decoding of nested linear codes. Our approach generalizes the results of Körner and Marton to computing an arbitrary number of linear combinations and to the lossy computation setting.

We present a practical strategy that aims to attain rate points on the dominant face of the multiple access channel capacity using a standard low complexity decoder. This technique is built upon recent theoretical developments of Zhu and Gastpar on compute-forward multiple access which achieves the capacity of the multiple access channel using a sequential decoder. We illustrate this strategy with off-the-shelf LDPC codes. In the first stage of decoding, the receiver first recovers a linear combination of the transmitted codewords using the sum-product algorithm (SPA). In the second stage, by using the recovered sum-of-codewords as side information, the receiver recovers one of the two codewords using a modified SPA, ultimately recovering both codewords. The main benefit of recovering the sum-of-codewords instead of the codeword itself is that it allows to attain points on the dominant face of the multiple access channel capacity without the need of rate-splitting or time sharing while maintaining a low complexity in the order of a standard point-to-point decoder. This property is also shown to be crucial for some applications, e.g., interference channels. For all the simulations with single-layer binary codes, our proposed practical strategy is shown to be within 1.7 dB of the theoretical limits, without explicit optimization on the off-the-self LDPC codes.

This paper presents a joint typicality framework for encoding and decoding nested linear codes in multi-user networks. This framework provides a new perspective on compute-forward within the context of discrete memoryless networks. In particular, it establishes an achievable rate region for computing a linear combination over a discrete memoryless multiple-access channel (MAC). When specialized to the Gaussian MAC, this rate region recovers and improves upon the lattice-based compute-forward rate region of Nazer and Gastpar, thus providing a unified approach for discrete memoryless and Gaussian networks. Furthermore, our framework provides some valuable insights on establishing the optimal decoding rate region for compute-forward by considering joint decoders, progressing beyond most previous works that consider successive cancellation decoding. Specifically, this paper establishes an achievable rate region for simultaneously decoding two linear combinations of nested linear codewords from K senders.

Recent work has employed joint typicality encoding and decoding of nested linear code ensembles to generalize the compute-forward strategy to discrete memoryless multiple-access channels (MACs). An appealing feature of these nested linear code ensembles is that the coding strategies and error probability bounds are conceptually similar to classical techniques for random i.i.d. code ensembles. In this paper, we consider the problem of recovering K linearly independent combinations over a K-user MAC, i.e., recovering the messages in their entirety via nested linear codes. While the MAC rate region is well-understood for random i.i.d. code ensembles, new techniques are needed to handle the statistical dependencies between competing codeword K-tuples that occur in nested linear code ensembles.

Inspired by the compute-and-forward scheme from Nazer and Gastpar, a novel multiple-access scheme introduced by Zhu and Gastpar makes use of nested lattice codes and sequential decoding of linear combinations of codewords to recover the individual messages. This strategy, coined compute-forward multiple access (CFMA), provably achieves points on the dominant face of the multiple-access capacity region while circumventing the need of time sharing or rate splitting. For a two-user multiple-access channel (MAC), we propose a practical procedure to design suitable codes from off-the-shelf LDPC codes and present a sequential belief propagation decoder with complexity comparable with that of point-to-point decoders. We demonstrate the potential of our strategy by comparing several numerical evaluations with theoretical limits.

We consider a setup in which confidential i.i.d. samples X1, ..., Xnfrom an unknown discrete distribution PXare passed through a discrete memoryless privatization channel (a.k.a. mechanism) which guarantees an ϵ-level of local differential privacy. For a given ϵ, the channel should be designed such that an estimate of the source distribution based on the channel outputs converges as fast as possible to the exact value PX. For this purpose we consider two metrics of estimation accuracy: the expected mean-square error and the expected Kullback-Leibler divergence. We derive their respective normalized first-order terms (as n → ∞), which for a given target privacy ϵ represent the factor by which the sample size must be augmented so as to achieve the same estimation accuracy as that of an identity (non-privatizing) channel. We formulate the privacy-utility tradeoff problem as being that of minimizing said first-order term under a privacy constraint ϵ. A converse bound is stated which bounds the optimal tradeoff away from the origin. Inspired by recent work on the optimality of staircase mechanisms (albeit for objectives different from ours), we derive an achievable tradeoff based on circulant step mechanisms. Within this finite class, we determine the optimal step pattern.

Most performance measures of pilot-assisted multiple-input multiple-output systems are functions of the linear precoder and the pilot sequence. A framework for the optimization of these two parameters is proposed, based on a matrix-valued generalization of the concept of effective signal-to-noise ratio (SNR) introduced in the famous work by Hassibi and Hochwald. Our framework aims to extend the work of Hassibi and Hochwald by allowing for transmit-side fading correlations, and by considering a class of utility functions of said effective SNR matrix, most notably including the well-known capacity lower bound used by Hassibi and Hochwald. We tackle the joint optimization problem by recasting the optimization of the precoder (resp. pilot sequence) subject to a fixed pilot sequence (resp. precoder) into a convex problem. Furthermore, we prove that joint optimality requires that the eigenbases of the precoder and pilot sequence be both aligned along the eigenbasis of the channel correlation matrix. We finally describe how to wrap all studied subproblems into an iteration that converges to a local optimum of the joint optimization.

In this paper, the operation of a licensed shared access system is investigated, considering downlink communication. The system comprises a multiple-input-single-output (MISO) incumbent transmitter (TX)-receiver (RX) pair, which offers a spectrum sharing opportunity to a MISO licensee TX-RX pair. Our main contribution is the design of a coordinated transmission scheme, inspired by the underlay cognitive radio (CR) approach, with the aim of maximizing the average rate of the licensee, subject to an average rate constraint for the incumbent. In contrast to most prior works on the underlay CR, the coordination of the two TXs takes place under a realistic channel state information (CSI) scenario, where each TX has solely access to the instantaneous direct channel of its served terminal. Such a CSI knowledge setting brings about a formulation based on the theory of Team Decisions, whereby the TXs aim at optimizing a common objective given the same constraint set, on the basis of individual channel information. Consequently, a novel set of applicable precoding schemes consisting in letting the two TXs cooperate on the basis of the statistical information is proposed. We verify by simulations that this novel, practically relevant, coordinated precoding scheme outperforms the standard underlay CR approach.

For fast-fading memoryless single-user channels, we present new rate expressions that are achievable with i.i.d. Gaussian codes and successive nearest-neighbor decoders based on a Euclidian distance metric. The use of successive decoding is motivated by two factors: firstly, it was recently discovered that successive decoding potentially enhances achievable rates on single-user channels with imperfect channel-state information at the receiver (semicoherent channels); secondly, in the limit as the number of decoding steps tends to infinity, some of these rate expressions become tractable and expressible as integrals. To offer a unified view, we choose to put all rate expressions-old and new-into this integral representation inspired by the infinitesimal successive-decoding approach, in order to unveal their similarities.

As shown by Médard, the capacity of fading channels with imperfect channel-state information can be lower-bounded by assuming a Gaussian channel input X with power P and by upper-bounding the conditional entropy h(X|Y, Ĥ) by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating X from (Y, Ĥ). We demonstrate that, using a rate-splitting approach, this lower bound can be sharpened: by expressing the Gaussian input X as the sum of two independent Gaussian variables X1and X2and by applying Médard's lower bound first to bound the mutual information between X1and Y while treating X2as noise, and by applying it a second time to the mutual information between X2and Y while assuming X1to be known, we obtain a capacity lower bound that is strictly larger than Médard's lower bound. We then generalize this approach to an arbitrary number L of layers, where X is expressed as the sum of L independent Gaussian random variables of respective variances Pℓ, ℓ = 1, ... , L summing up to P. Among all such rate-splitting bounds, we determine the supremum over power allocations Pℓand total number of layers L. This supremum is achieved for L →∞ and gives rise to an analytically expressible capacity lower bound. For Gaussian fading, this novel bound is shown to converge to the Gaussian-input mutual information as the signal-to-noise ratio (SNR) grows, provided that the variance of the channel estimation error H - Ĥ tends to zero as the SNR tends to infinity.

A well-established capacity lower bound of multiple-input multiple-output (MIMO) single-user fading channels operating with imperfect receiver-side channel-state information (CSI) is improved using a simple rate-splitting and successive-decoding scheme. The potential improvement is shown to increase with the number of allowed decoding steps (layers) to such extent that the best layering strategy is approached in the limit as the number of layers tends to infinity. We give a general analytic expression of this limit, which constitutes a new capacity lower bound that is sharper than the conventional bound. Using large random matrix theory, we derive an asymptotic approximation of this novel bound, which is shown via numerical simulation to be highly accurate over the whole range of signal-to-noise ratios.

We study the maximization of an achievable ergodic rate expression of a multiple-input single-output (MISO) channel where both ends are cognizant of the same erroneous estimate of the current fading state, yet they have complete knowledge of channel statistics. A training procedure estimates each channel state by means of dedicated pilot symbols whose sum energy is fixed, while for data transmission a fixed average energy per channel access (i.e., average power) is available. The optimization consists, on one hand, in finding the optimal beamforming strategy and temporal power control policy, and on the other hand, in optimally constructing the pilot sequence according to the channel's correlation structure.

For single-user MIMO channels with partial re ceiver CSI, we study the difference between a lower bound and two alternative upper bounds of the mutual information achieved with Gaussian codebooks. These differences are termed bound gaps Δ and δ, respectively. The latter may serve to derive a capacity bound gap. In contrast to previous studies, we assume that the channel estimation error statistics are not given a priori, but depend on the parameters of a training routine, in which a pilot sequence is transmitted, and where the channel realization is linearly estimated. Under these conditions, we successively determine analytic upper and lower bounds on the mutual information bound gap Δ. We further study the asymptotic behavior of said bound gaps for high SNR and a large number of antennas. This allows us to prove, for example, that for MISO channels and a certain class of semicorrelated MIMO channels, when the training and transmit power levels are equal, the capacity is approached to within min(NT, NR) bits by the capacity bounds, where NTand NRstand for the number of transmit and receive antennas, respectively.

For single-user, multiple-input multiple-output (MIMO) channels with Rayleigh fading correlated at the transmitter side, and where the receiver only has partial channel knowledge in form of an MMSE channel estimate, we study the joint optimization of the linear precoder and the pilot (training) sequence under the constraint of prescribed transmit power and training energy budgets. Although this joint problem is generally not convex itself, we can show that the two marginal problems of optimizing either the pilot sequence or the precoder when the other variable is fixed, are convex. Furthermore, we characterize the jointly optimal transmit and training directions. Finally, we propose a full characterization of the Pareto efficient joint power loading strategies for the case of two transmit antennas, and illustrate the behavior of the jointly optimal solution.