We discuss the possibility of a relativistic relationship between information and entropy, closely analogous to the classical Maxwell electro-magnetic wave equations. Inherent to the analysis is the description of information as residing in points of non-analyticity; yet ultimately also exhibiting a distributed characteristic: additionally analogous, therefore, to the wave-particle duality of light. At cosmological scales our vector differential equations predict conservation of information in black holes, whereas regular- and Z-DNA molecules correspond to helical solutions at microscopic levels. We further propose that regular- and Z-DNA are equivalent to the alternative words chosen from an alphabet to maintain the equilibrium of an information transmission system.

The improvements in coverage through spatial diversity and increased data rates through spatial multiplexing using a distributed multiple-input multiple-output (MIMO) system are important targets for future wireless communications. Here, the appropriate separation of remote antenna units (RAUs) at several user locations in a millimeter-wave system is demonstrated. An analog radio-over-fiber (RoF) fronthaul is used to achieve flexible spacing of distributed RAUs and transports two Gb/s data streams over 2.2 km of fiber and up to 8 m of 60 GHz wireless transmission distance. A performance comparison is performed between single-input single-output and MIMO operation using different antenna spacing and transmission distance. Results show that the wider RAU spacing enabled by the RoF distribution provides improved results at longer distances, for both spatial diversity and for spatial multiplexing. Verification of a method for measuring each channel coefficient individually and using subsequent MIMO processing on these coefficients enables an extension to the results showing the feasibility of 30 m indoor transmission.

To date the evolution from traditional distributed radio access networks (D-RAN) towards fronthaul oriented centralized (C-RAN) architectures has imposed significant challenges for the underlying transport network. The processing and coordination benefits anticipated in C-RAN are generally underpinned with the assumption of a full fiber transport network capable of meeting the demanding performance criteria of fronthaul transport. Recent advances in Ethernet based fronthaul interfaces together with exploration of new mmWave and sub-THz spectrum bands present an opportunity for wireless solutions to also realize these fronthaul transport requirements. In this work, the requirements for promising new Ethernet based fronthaul interfaces are explored. These requirements are assessed against the measured capabilities of a state-of-the-art E-band (71-86 GHz) wireless transport solution. The experimental results are then used to forecast the performance expectations of future higher bandwidth systems operating above 100 GHz. A dimensioning and link budget analysis is performed for the various candidate spectrum bands and fronthaul interfaces to highlight the viability of fronthaul delivered over wireless transport. Finding show that transport solutions operating at mmWave and sub-THz frequencies are able to support the performance requirements of newly standardized fronthaul interface splits and as such present an opportunity to utilize wireless fronthaul transport in C-RAN architectures where fiber cannot otherwise be supported. Furthermore, analysis demonstrates that the hop lengths possible for 5G small cell configurations are well aligned with the expected inter-site distances of future dense urban cell deployments making wireless fronthaul a promising concept for realizing future C-RAN based cell densification.

Purpose in systems is considered to be beyond the purview of science since it is thought to be intrinsically personal. However, just as Claude Shannon was able to define an impersonal measure of information, so we formally define the (impersonal) ‘entropic purpose’ of an information system (using the theoretical apparatus of Quantitative Geometrical Thermodynamics) as the line integral of an entropic “purposive” Lagrangian defined in hyperbolic space across the complex temporal plane. We verify that this Lagrangian is well-formed: it has the appropriate variational (Euler-Lagrange) behaviour. We also discuss the teleological characteristics of such variational behaviour (featuring both thermodynamically reversible and irreversible temporal measures), so that a “Principle of Least (entropic) Purpose” can be adduced for any information-producing system. We show that entropic purpose is (approximately) identified with the information created by the system: an empirically measurable quantity. Exploiting the relationship between the entropy production of a system and its energy Hamiltonian, we also show how Landauer’s principle also applies to the creation of information; any purposive system that creates information will also dissipate energy. Finally, we discuss how ‘entropic purpose’ might be applied in artificial intelligence contexts (where degrees of system ‘aliveness’ need to be assessed), and in cybersecurity (where this metric for ‘entropic purpose’ might be exploited to help distinguish between people and bots).

We prove that the probability of “A or B”, denoted as p(A or B), where A and B are events or hypotheses that may be recursively dependent, is given by a “Hyperbolic Sum Rule” (HSR), which is relationally isomorphic to the hyperbolic tangent double-angle formula. We also prove that this HSR is Maximum Entropy (MaxEnt). Since this recursive dependency is commutative, it maintains the symmetry between the two events, while the recursiveness also represents temporal symmetry within the logical structure of the HSR. The possibility of recursive probabilities is excluded by the “Conventional Sum Rule” (CSR), which we have also proved to be MaxEnt (with lower entropy than the HSR due to its narrower domain of applicability). The concatenation property of the HSR is exploited to enable analytical, consistent, and scalable calculations for multiple hypotheses. Although they are intrinsic to current artificial intelligence and machine learning applications, such calculations are not conveniently available for the CSR, moreover they are presently considered intractable for analytical study and methodological validation. Where, for two hypotheses, we have p(A|B) > 0 and p(B|A) > 0 together (where “A|B” means “A given B”), we show that either {A,B} is independent or {A,B} is recursively dependent. In general, recursive relations cannot be ruled out: the HSR should be used by default. Because the HSR is isomorphic to other physical quantities, including those of certain components that are important for digital signal processing, we also show that it is as reasonable to state that “probability is physical” as it is to state that “information is physical” (which is now recognised as a truism of communications network engineering); probability is not merely a mathematical construct. We relate this treatment to the physics of Quantitative Geometrical Thermodynamics, which is defined in complex hyperbolic (Minkowski) spacetime.

This paper presents mobile network deployment analysis aimed at understanding the use of high frequency wireless fronthaul links to realize dense cell network architectures. A high resolution digital twin model is built based on real-world data sets to identify line-of-sight propagation paths between existing macro cell roof top sites and lamp post infrastructure locations suitable for new street level cell sites. The resulting line-of-sight path topology is used to simulate wireless fronthaul links based on industry standardized fronthaul interfaces across the urban environment. In considering the stringent fronthaul interface requirements for a representative 5G radio configuration, the suitability of emerging mmWave and sub-THz transport bands between 71.124 and 174.8 GHz to fulfill the wireless fronthaul centralized RAN deployment is analyzed. Findings in this work have demonstrated that with the right combination of fronthaul interface and spectrum band upto 73% of new street level cell sites in a dense deployment could be built using a wireless fronthaul transport solution.