Information Theory (cs.IT)

Abstract: This paper considers the distributed information bottleneck (D-IB) problem for a primitive Gaussian diamond channel with two relays and MIMO Rayleigh fading. The channel state is an independent and identically distributed (i.i.d.) process known at the relays but unknown to the destination. The relays are oblivious, i.e., they are unaware of the codebook and treat the transmitted signal as a random process with known statistics. The bottleneck constraints prevent the relays to communicate the channel state information (CSI) perfectly to the destination. To evaluate the bottleneck rate, we provide an upper bound by assuming that the destination node knows the CSI and the relays can cooperate with each other, and also two achievable schemes with simple symbol-by-symbol relay processing and compression. Numerical results show that the lower bounds obtained by the proposed achievable schemes can come close to the upper bound on a wide range of relevant system parameters.

Abstract: We study a data-driven approach to the bee identification problem for DNA strands. The bee-identification problem, introduced by Tandon et al. (2019), requires one to identify $M$ bees, each tagged by a unique barcode, via a set of $M$ noisy measurements. Later, Chrisnata et al. (2022) extended the model to case where one observes $N$ noisy measurements of each bee, and applied the model to address the unordered nature of DNA storage systems. In such systems, a unique address is typically prepended to each DNA data block to form a DNA strand, but the address may possibly be corrupted. While clustering is usually used to identify the address of a DNA strand, this requires $\mathcal{M}^2$ data comparisons (when $\mathcal{M}$ is the number of reads). In contrast, the approach of Chrisnata et al. (2022) avoids data comparisons completely. In this work, we study an intermediate, data-driven approach to this identification task. For the binary erasure channel, we first show that we can almost surely correctly identify all DNA strands under certain mild assumptions. Then we propose a data-driven pruning procedure and demonstrate that on average the procedure uses only a fraction of $\mathcal{M}^2$ data comparisons. Specifically, for $\mathcal{M}= 2^n$ and erasure probability $p$, the expected number of data comparisons performed by the procedure is $\kappa\mathcal{M}^2$, where $\left(\frac{1+2p-p^2}{2}\right)^n \leq \kappa \leq \left(\frac{1+p}{2}\right)^n $.

Abstract: In this paper, we study the computation of the rate-distortion-perception function (RDPF) for discrete memoryless sources subject to a single-letter average distortion constraint and a perception constraint that belongs to the family of f-divergences. For that, we leverage the fact that RDPF, assuming mild regularity conditions on the perception constraint, forms a convex programming problem. We first develop parametric characterizations of the optimal solution and utilize them in an alternating minimization approach for which we prove convergence guarantees. The resulting structure of the iterations of the alternating minimization approach renders the implementation of a generalized Blahut-Arimoto (BA) type of algorithm infeasible. To overcome this difficulty, we propose a relaxed formulation of the structure of the iterations in the alternating minimization approach, which allows for the implementation of an approximate iterative scheme. This approximation is shown, via the derivation of necessary and sufficient conditions, to guarantee convergence to a globally optimal solution. We also provide sufficient conditions on the distortion and the perception constraints which guarantee that our algorithm converges exponentially fast. We corroborate our theoretical results with numerical simulations, and we draw connections with existing results.

Abstract: We present a new class of private information retrieval (PIR) schemes that keep the identity of the file requested private in the presence of at most $t$ colluding servers, based on the recent framework developed for such $t$-PIR schemes using star products of transitive codes. These $t$-PIR schemes employ the class of Berman codes as the storage-retrieval code pairs. Berman codes, which are binary linear codes of length $n^m$ for any $n\geq 2$ and $m\geq 1$ being positive integers, were recently shown to achieve the capacity of the binary erasure channel. We provide a complete characterization of the star products of the Berman code pairs, enabling us to calculate the PIR rate of the star product-based schemes that employ these codes. The schemes we present have flexibility in the number of servers, the PIR rate, the storage rate, and the collusion parameter $t$, owing to numerous codes available in the class of Berman codes.

Abstract: This paper analyzes the performance of the 3rd Generation Partnership Project (3GPP)-inspired multi-cell wideband single-hop backhaul millimeter-wave-in-band-full-duplex (IBFD)-integrated access and backhaul (IAB) networks by using stochastic geometry. We model the wired-connected Next Generation NodeBs (gNBs) as the Mat\'ern hard-core point process (MHCPP) to meet the real-world deployment requirement and reduce the cost caused by wired connection in the network. We first derive association probabilities that reflect how likely the typical user-equipment is served by a gNB or an IAB-node based on the maximum long-term averaged biased-received-desired-signal power criteria. Further, by leveraging the composite Gamma-Lognormal distribution, we derive the closed-form signal to interference plus noise ratio coverage, capacity with outage, and ergodic capacity of the network. In order to avoid underestimating the noise, we consider the sidelobe gain on inter-cell interference links and the analog to digital converter quantization noise. Compared with the half-duplex transmission, numerical results show an enhanced capacity with outage and ergodic capacity provided by IBFD under successful self-interference cancellation. We also study how the power bias and density ratio of the IAB-node to gNB, and the hard-core distance can affect system performances.

Abstract: Reconfigurable intelligent surfaces (RISs) with their potential of enabling a programmable environment comprise a promising technology to support the coexistence of enhanced mobile broadband (eMBB) and ultra-reliable-low-latency communication (URLLC) services. In this paper, we propose a RIS-assisted scheme for multiplexing hybrid eMBB-URLLC uplink traffic. Specifically, the scheme relies on the computation of two RIS configurations, given that only eMBB channel state information (CSI) is available. The first configuration optimizes the eMBB quality of service, while the second one mitigates the eMBB interference in the URLLC traffic. Analyzing the outage probability achieved by the scheme, we demonstrate that a RIS can improve the reliability of URLLC transmissions even in the absence of URLLC CSI.

Abstract: Maximum-distance separable (MDS) convolutional codes are characterized by the property that their free distance reaches the generalized Singleton bound. In this paper, new criteria to construct MDS convolutional codes are presented. Additionally, the obtained convolutional codes have optimal first (reverse) column distances and the criteria allow to relate the construction of MDS convolutional codes to the construction of reverse superregular Toeplitz matrices. Moreover, we present some construction examples for small code parameters over small finite fields.

Abstract: There exists a large literature of construction of convolutional codes with maximal or near maximal free distance. Much less is known about constructions of convolutional codes having optimal or near optimal column distances. In this paper, a new construction of convolutional codes over the binary field with optimal column distances is presented.

Abstract: Golay complementary set (GCS) plays a vital role in reducing peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency division multiplexing (OFDM). A more general version of GCS is a multiple shift complementary set (MSCS), where by relaxing the condition of zero auto-correlation sum throughout all the non-zero time shifts to the integer multiples of some fixed time shift, more sequence sets can be made available. In this paper, we propose direct constructions of MSCSs with flexible and arbitrary lengths and flexible set sizes, by using multivariable functions, which have not been reported before.

Abstract: Maximum distance separable convolutional codes are characterized by the property that the free distance reaches the generalized Singleton bound, which makes them optimal for error correction. However, the existing constructions of such codes are available over fields of large size. In this paper, we present the unique construction of MDS convolutional codes of rate $1/2$ and degree $5$ over the field $\mathbb{F}_{11}$.

Abstract: We study the problem of overcoming exponential sample complexity in differential entropy estimation under Gaussian convolutions. Specifically, we consider the estimation of the differential entropy $h(X+Z)$ via $n$ independently and identically distributed samples of $X$, where $X$ and $Z$ are independent $D$-dimensional random variables with $X$ subgaussian with bounded second moment and $Z\sim\mathcal{N}(0,\sigma^2I_D)$. Under the absolute-error loss, the above problem has a parametric estimation rate of $\frac{c^D}{\sqrt{n}}$, which is exponential in data dimension $D$ and often problematic for applications. We overcome this exponential sample complexity by projecting $X$ to a low-dimensional space via principal component analysis (PCA) before the entropy estimation, and show that the asymptotic error overhead vanishes as the unexplained variance of the PCA vanishes. This implies near-optimal performance for inherently low-dimensional structures embedded in high-dimensional spaces, including hidden-layer outputs of deep neural networks (DNN), which can be used to estimate mutual information (MI) in DNNs. We provide numerical results verifying the performance of our PCA approach on Gaussian and spiral data. We also apply our method to analysis of information flow through neural network layers (c.f. information bottleneck), with results measuring mutual information in a noisy fully connected network and a noisy convolutional neural network (CNN) for MNIST classification.

Abstract: Abstract: In this article, we will analyze in detail the coding limit of an individual sequence by introducing the latest developments brought by the Set Shaping Theory. This new theory made us realize that there is a huge difference between source entropy and zero order empirical entropy. Understanding the differences between these two variables allows us to take an important step forward in the study of the compression limit of an individual sequence, which we know is not calculable.

Abstract: Mobile edge computing (MEC) enables resource-limited IoT devices to complete computation-intensive or delay-sensitive task by offloading the task to adjacent edge server deployed at the base station (BS), thus becoming an important technology in 5G and beyond. Due to channel occlusion, some users may not be able to access the computation capability directly from the BS. Confronted with this issue, many other devices in the MEC system can serve as cooperative nodes to collect the tasks of these users and further forward them to the BS. In this paper, we study a MEC system in which multiple users continuously generate the tasks and offload the tasks to the BS through a cooperative node. As the tasks are continuously generated, users should simultaneously execute the task generation in the current time frame and the task offloading of the last time frame, i.e. the task is processed in a streaming model. To optimize the power consumption of the users and the cooperative node for finishing these streaming tasks, we investigate the duration of each step in finishing the tasks together with multiuser offloading ratio and bandwidth allocation within two cases: the BS has abundant computation capacity (Case I) and the BS has limited computation capacity (Case II). For both cases, the formulated optimization problems are nonconvex due to fractional structure of the objective function and complicated variable coupling. To address this issue, we propose optimal solution algorithm with low complexity. Finally, simulation is carried out to verify the effectiveness of the proposed methods and reveal the performance of the considered system.

Abstract: Optical Wireless Communication networks (OWC) has emerged as a promising technology that enables high-speed and reliable communication bandwidth for a variety of applications. In this work, we investigated applying Random Linear Network Coding (RLNC) over NOMA-based OWC networks to improve the performance of the proposed high density indoor optical wireless network where users are divided into multicast groups, and each group contains users that slightly differ in their channel gains. Moreover, a fixed power allocation strategy is considered to manage interference among these groups and to avoid complexity. The performance of the proposed RLNC-NOMA scheme is evaluated in terms of average bit error rate and ergodic sum rate versus the power allocation ratio factor. The results show that the proposed scheme is more suitable for the considered network compared to the traditional NOMA and orthogonal transmission schemes.

Abstract: We consider a network of $n$ user nodes that receives updates from a source and employs an age-based gossip protocol for faster dissemination of version updates to all nodes. When a node forwards its packet to another node, the packet information gets mutated with probability $p$ during transmission, creating misinformation. The receiver node does not know whether an incoming packet information is different from the packet information originally at the sender node. We assume that truth prevails over misinformation, and therefore, when a receiver encounters both accurate information and misinformation corresponding to the same version, the accurate information gets chosen for storage at the node. We study the expected fraction of nodes with correct information in the network and version age at the nodes in this setting using stochastic hybrid systems (SHS) modelling and study their properties. We observe that very high or very low gossiping rates help curb misinformation, and misinformation spread is higher with moderate gossiping rates. We support our theoretical findings with simulation results which shed further light on the behavior of above quantities.