Characterization of the Complexity of Computing the Capacity of Colored Noise Gaussian Channels

This paper explores the computational complexity involved in determining the capacity of the band-limited additive colored Gaussian noise (ACGN) channel and its capacity-achieving power spectral density (p.s.d.). The study reveals that when the noise p.s.d. is a strictly positive computable continuous function, computing the capacity of the band-limited ACGN channel becomes a $\#\mathrm{P}_1$-complete problem within the set of polynomial time computable noise p.s.d.s. Meaning that it is even more complex than problems that are $\mathrm{NP}_1$-complete. Additionally, it is shown that the capacity-achieving distribution is also $\#\mathrm{P}_1$-complete. Furthermore, under the widely accepted assumption that $\mathrm{FP}_1 \neq \#\mathrm{P}_1$, it has two significant implications for the ACGN channel. The first implication is the existence of a polynomial time computable noise p.s.d. for which the computation of its capacity cannot be performed in polynomial time, i.e., the number of computational steps on a Turing Machine grows faster than all polynomials. The second one is the existence of a polynomial time computable noise p.s.d. for which determining its capacity-achieving p.s.d. cannot be done within polynomial time

Transformer-aided Wireless Image Transmission with Channel Feedback

This paper presents a novel wireless image transmission paradigm that can exploit feedback from the receiver, called DeepJSCC-ViT-f. We consider a block feedback channel model, where the transmitter receives noiseless/noisy channel output feedback after each block. The proposed scheme employs a single encoder to facilitate transmission over multiple blocks, refining the receiver's estimation at each block. Specifically, the unified encoder of DeepJSCC-ViT-f can leverage the semantic information from the source image, and acquire channel state information and the decoder's current belief about the source image from the feedback signal to generate coded symbols at each block. Numerical experiments show that our DeepJSCC-ViT-f scheme achieves state-of-the-art transmission performance with robustness to noise in the feedback link. Additionally, DeepJSCC-ViT-f can adapt to the channel condition directly through feedback without the need for separate channel estimation. We further extend the scope of the DeepJSCC-ViT-f approach to include the broadcast channel, which enables the transmitter to generate broadcast codes in accordance with signal semantics and channel feedback from individual receivers

Beyond Transmitting Bits: Context, Semantics, and Task-Oriented Communications

Communication systems to date primarily aim at reliably communicating bit sequences. Such an approach provides efficient engineering designs that are agnostic to the meanings of the messages or to the goal that the message exchange aims to achieve. Next generation systems, however, can be potentially enriched by folding message semantics and goals of communication into their design. Further, these systems can be made cognizant of the context in which communication exchange takes place, providing avenues for novel design insights. This tutorial summarizes the efforts to date, starting from its early adaptations, semantic-aware and task-oriented communications, covering the foundations, algorithms and potential implementations. The focus is on approaches that utilize information theory to provide the foundations, as well as the significant role of learning in semantics and task-aware communications.Comment: 28 pages, 14 figure

Secure, reliable, and efficient communication over the wiretap channel

Secure wireless communication between devices is essential for modern communication systems. Physical-layer security over the wiretap channel may provide an additional level of secrecy beyond the current cryptographic approaches. Given a sender Alice, a legitimate receiver Bob, and a malicious eavesdropper Eve, the wiretap channel occurs when Eve experiences a worse signal-to-noise ratio than Bob. Previous study of the wiretap channel has tended to make assumptions that ignore the reality of wireless communication. This thesis presents a study of short block length codes with the aim of both reliability for Bob and confusion for Eve. The standard approach to wiretap coding is shown to be very inefficient for reliability. Quantifying Eve's confusion in terms of entropy is not solved in many cases, though it is possible for codes with a moderate complexity trellis representation. Using error rate arguments, error correcting codes with steep performance curves turn out to be desirable both for reliability and confusion.Masteroppgave i informatikkINF399MAMN-INFMAMN-PRO

Information theoretic limits of MIMO wireless networks with bounded input and imperfect CSIT

In this thesis, we investigate some information theoretic limits of two specific types of MIMO wireless networks. In the first one, the effect of channel uncertainty at the transmitter (due to estimation error, feedback latency, and so on) in MIMO broadcast channels is investigated. In this setting, we capture this imperfectness in the bounds for the DoF region of the channel. The second one is the point to point deterministic MIMO channel with input amplitude constraint. For certain settings, the capacity of this channel is derived, while for the general problem, upper and lower bounds for the capacity are obtained.Open Acces

Deep Autoencoder-based Z-Interference Channels with Perfect and Imperfect CSI

A deep autoencoder (DAE)-based structure for endto-end communication over the two-user Z-interference channel (ZIC) with finite-alphabet inputs is designed in this paper. The proposed structure jointly optimizes the two encoder/decoder pairs and generates interference-aware constellations that dynamically adapt their shape based on interference intensity to minimize the bit error rate (BER). An in-phase/quadrature-phase (I/Q) power allocation layer is introduced in the DAE to guarantee an average power constraint and enable the architecture to generate constellations with nonuniform shapes. This brings further gain compared to standard uniform constellations such as quadrature amplitude modulation. The proposed structure is then extended to work with imperfect channel state information (CSI). The CSI imperfection due to both the estimation and quantization errors are examined. The performance of the DAEZIC is compared with two baseline methods, i.e., standard and rotated constellations. The proposed structure significantly enhances the performance of the ZIC both for the perfect and imperfect CSI. Simulation results show that the improvement is achieved in all interference regimes (weak, moderate, and strong) and consistently increases with the signal-to-noise ratio (SNR). For example, more than an order of magnitude BER reduction is obtained with respect to the most competitive conventional method at weak interference when SNR>15dB and two bits per symbol are transmitted. The improvements reach about two orders of magnitude when quantization error exists, indicating that the DAE-ZIC is more robust to the interference compared to the conventional methods.Comment: 13 pages, 13 figures, 2 tables. Accepted for publication in the IEEE Transactions on Communications. arXiv admin note: text overlap with arXiv:2303.0831

Purposeful Co-Design of OFDM Signals for Ranging and Communications

This paper analyzes the fundamental trade-offs that occur in the co-design of orthogonal frequency-division multiplexing signals for both ranging (via time-of-arrival estimation) and communications. These trade-offs are quantified through the Shannon capacity bound, probability of outage, and the Ziv-Zakai bound on range estimation variance. Bounds are derived for signals experiencing frequency-selective Rayleigh block fading, accounting for the impact of limited channel knowledge and multi-antenna reception. Uncompensated carrier frequency offset and phase errors are also factored into the capacity bounds. Analysis based on the derived bounds demonstrates how Pareto-optimal design choices can be made to optimize the communication throughput, probability of outage, and ranging variance. Different signal design strategies are then analyzed, showing how Pareto-optimal design choices change depending on the channel

On Cyclic Delay Diversity OFDM Based Channels

Orthogonal Frequency Division Multiplexing, so called OFDM, has found a prominent place in various wireless systems and networks as a method of encoding data over multiple carrier frequencies. OFDM-based communication systems, however, lacking inherent diversity, are capable of benefiting from different spatial diversity schemes. One such scheme, Cyclic Delay Diversity (CDD) is a method to provide spatial diversity which can be also interpreted as a Space-Time Block Coding (STBC) step. The main idea is to add more transmit antennas at the transmitter side sending the same streams of data, though with differing time delays. In [1], the capacity of a point-to-point OFDM-based channel with CDD is derived for inputs with Gaussian and discrete constellations. In this dissertation, we use the same approach for an OFDM-based single-input single-output (SISO) two-user interference channel (IC). In our model, at the receiver side, the interference is treated as noise. Moreover, since the channel is time-varying (slow-fading), the Shannon capacity in the strict sense is not well-defined, so the expected value of the instantaneous capacity is calculated instead. Furthermore, the channel coefficients are unknown to the transmitters. Thus, in this setting, the probability of outage emerges as a reasonable performance measure. Adding an extra antenna in the transmitters, the SISO IC turns into an MISO IC, which results in increasing the diversity. Both the continuous and discrete inputs are studied and it turns out that decoding interference is helpful in some cases. The results of the simulations for discrete inputs indicate that there are improvements in terms of outage capacity compared to the ICs with single-antenna transmitters

Analysis and Design of Line of Sight MIMO transmission systems

A cost-effective solution to the problem of guaranteeing backhaul connectivity in mobile cellular networks is the use of point-to-point microwave links in the Q-Band and E-Band. The always increasing rate in mobile data traffic makes these microwave radio links a potential bottleneck in the deployment of high-throughput cellular networks. A fundamental way to characterize the impact of phase noise on the throughput of these systems is to study their Shannon capacity. Unfortunately, the capacity of the phase-noise channel is not known in closed-form, even for simple channel models. The effect of phase noise in telecommunication systems is more evident in presence of multiple antennas at transmitter and receiver because of the overlapping of phase noise contribution in receivers. We propose a simulated-based tool to compute a lower bound to channel capacity for SISO and MIMO systems in presence of phase noise with one oscillator shared among the antennas per side and we give a non asymptotic expression of an upper bound to capacity always for SISO and MIMO channels. Finally we present a low complex phase detector based on combination of Phase Locked Loop (PLL) exploiting the decisions made by a turbo decoder. The aim of this work is showing a way to bound the channel capacity for single antenna and multiple antennas channels impaired by phase noise generated by instabilities in oscillators driving all the transceivers, and compare the performance of the proposed phase detector to those theoretical limits