This paper analyses the multiplexing gain (MG) achievable over Wyners symmetric network with random user activity and random arrival of mixed-delay traffic. The mixed-delay traffic is composed of delay-tolerant traffic and delay-sensitive traffic whe
re only the former can benefit from transmitter and receiver cooperation since the latter is subject to stringent decoding delays. The total number of cooperation rounds at transmitter and receiver sides is limited to $D$ rounds. We derive inner and outer bounds on the MG region. In the limit as $Dto infty$, the bounds coincide and the results show that transmitting delay-sensitive messages does not cause any penalty on the sum MG. For finite $D$ our bounds are still close and prove that the penalty caused by delay-sensitive transmissions is small.
We study communication systems over band-limited Additive White Gaussian Noise (AWGN) channels in which the transmitter output is constrained to be symmetric binary (bi-polar). In this work we improve the original Ozarov-Wyner-Ziv (OWZ) lower bound o
n capacity by introducing a new achievability scheme with two advantages over the studied OWZ scheme which is based on peak-power constrained pulse-amplitude modulation. Our scheme achieves a moderately improved information rate and it does so with much less sign transitions of the binary signal. The gap between the known upper-bound based on spectral constrains of bi-polar signals and our achievable lower bound is reduced to 0.86 bits per Nyquist interval at high SNR.
This work considers a Poisson noise channel with an amplitude constraint. It is well-known that the capacity-achieving input distribution for this channel is discrete with finitely many points. We sharpen this result by introducing upper and lower bo
unds on the number of mass points. Concretely, an upper bound of order $mathsf{A} log^2(mathsf{A})$ and a lower bound of order $sqrt{mathsf{A}}$ are established where $mathsf{A}$ is the constraint on the input amplitude. In addition, along the way, we show several other properties of the capacity and capacity-achieving distribution. For example, it is shown that the capacity is equal to $ - log P_{Y^star}(0)$ where $P_{Y^star}$ is the optimal output distribution. Moreover, an upper bound on the values of the probability masses of the capacity-achieving distribution and a lower bound on the probability of the largest mass point are established. Furthermore, on the per-symbol basis, a nonvanishing lower bound on the probability of error for detecting the capacity-achieving distribution is established under the maximum a posteriori rule.
Consider a channel ${bf Y}={bf X}+ {bf N}$ where ${bf X}$ is an $n$-dimensional random vector, and ${bf N}$ is a Gaussian vector with a covariance matrix ${bf mathsf{K}}_{bf N}$. The object under consideration in this paper is the conditional mean of
${bf X}$ given ${bf Y}={bf y}$, that is ${bf y} to E[{bf X}|{bf Y}={bf y}]$. Several identities in the literature connect $E[{bf X}|{bf Y}={bf y}]$ to other quantities such as the conditional variance, score functions, and higher-order conditional moments. The objective of this paper is to provide a unifying view of these identities. In the first part of the paper, a general derivative identity for the conditional mean is derived. Specifically, for the Markov chain ${bf U} leftrightarrow {bf X} leftrightarrow {bf Y}$, it is shown that the Jacobian of $E[{bf U}|{bf Y}={bf y}]$ is given by ${bf mathsf{K}}_{{bf N}}^{-1} {bf Cov} ( {bf X}, {bf U} | {bf Y}={bf y})$. In the second part of the paper, via various choices of ${bf U}$, the new identity is used to generalize many of the known identities and derive some new ones. First, a simple proof of the Hatsel and Nolte identity for the conditional variance is shown. Second, a simple proof of the recursive identity due to Jaffer is provided. Third, a new connection between the conditional cumulants and the conditional expectation is shown. In particular, it is shown that the $k$-th derivative of $E[X|Y=y]$ is the $(k+1)$-th conditional cumulant. The third part of the paper considers some applications. In a first application, the power series and the compositional inverse of $E[X|Y=y]$ are derived. In a second application, the distribution of the estimator error $(X-E[X|Y])$ is derived. In a third application, we construct consistent estimators (empirical Bayes estimators) of the conditional cumulants from an i.i.d. sequence $Y_1,...,Y_n$.
We investigate the special case of diamond relay comprising a Gaussian channel with identical frequency response between the user and the relays and fronthaul links with limited rate from the relays to the destination. We use the oblivious compress a
nd forward (CF) with distributed compression and decode and forward (DF) where each relay decodes the whole message and sends half of its bits to the destination. We derive achievable rate by using time-sharing between DF and CF. The optimal time sharing proportion between DF and CF and power and rate allocations are different at each frequency and are fully determined.
This paper reviews the theoretical and practical principles of the broadcast approach to communication over state-dependent channels and networks in which the transmitters have access to only the probabilistic description of the time-varying states w
hile remaining oblivious to their instantaneous realizations. When the temporal variations are frequent enough, an effective long-term strategy is adapting the transmission strategies to the systems ergodic behavior. However, when the variations are infrequent, their temporal average can deviate significantly from the channels ergodic mode, rendering a lack of instantaneous performance guarantees. To circumvent a lack of short-term guarantees, the {em broadcast approach} provides principles for designing transmission schemes that benefit from both short- and long-term performance guarantees. This paper provides an overview of how to apply the broadcast approach to various channels and network models under various operational constraints.
A Fog-Radio Access Network (F-RAN) is studied in which cache-enabled Edge Nodes (ENs) with dedicated fronthaul connections to the cloud aim at delivering contents to mobile users. Using an information-theoretic approach, this work tackles the problem
of quantifying the potential latency reduction that can be obtained by enabling Device-to-Device (D2D) communication over out-of-band broadcast links. Following prior work, the Normalized Delivery Time (NDT) --- a metric that captures the high signal-to-noise ratio worst-case latency --- is adopted as the performance criterion of interest. Joint edge caching, downlink transmission, and D2D communication policies based on compress-and-forward are proposed that are shown to be information-theoretically optimal to within a constant multiplicative factor of two for all values of the problem parameters, and to achieve the minimum NDT for a number of special cases. The analysis provides insights on the role of D2D cooperation in improving the delivery latency.
The sectorized hexagonal model with mixed delay constraints is considered when both neighbouring mobile users and base stations can cooperate over rate-limited links. Each message is a combination of independent fast and slow bits, where the former a
re subject to a stringent delay constraint and cannot profit from cooperation. Inner and outer bounds on the multiplexing gain region are derived. The obtained results show that for small cooperation prelogs or moderate fast multiplexing gains, the overall performance (sum multiplexing gain) is hardly decreased by the stringent delay constraints on the fast bits. For large cooperation prelogs and large fast multiplexing gains, increasing the fast multiplexing gain by $Delta$ comes at the expense of decreasing the sum multiplexing gain by $3 Delta$.
The problem of channel coding over the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC) with additive independent Gaussian states is considered. The states are known in a noncausal manner to the encoder, and it wishes to minimize
the amount of information that the receivers can learn from the channel outputs about the state sequence. The state leakage rate is measured as a normalized blockwise mutual information between the state sequence and the channel outputs sequences. We employ a new version of a state-dependent extremal inequality and show that Gaussian input maximizes the state-dependent version of Martons outer bound. Further we show that our inner bound coincides with the outer bound. Our result generalizes previously studied scalar Gaussian BC with state and MIMO BC without state.
Device-to-Device (D2D) communication can support the operation of cellular systems by reducing the traffic in the network infrastructure. In this paper, the benefits of D2D communication are investigated in the context of a Fog-Radio Access Network (
F-RAN) that leverages edge caching and fronthaul connectivity for the purpose of content delivery. Assuming offline caching, out-of-band D2D communication, and an F-RAN with two edge nodes and two user equipments, an information-theoretically optimal caching and delivery strategy is presented that minimizes the delivery time in the high signal-to-noise ratio regime. The delivery time accounts for the latency caused by fronthaul, downlink, and D2D transmissions. The proposed optimal strategy is based on a novel scheme for an X-channel with receiver cooperation that leverages tools from real interference alignment. Insights are provided on the regimes in which D2D communication is beneficial.
