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Alex Grant

Publications and source records attributed to Alex Grant.

At least 19 recordsLinked to original sources
arXiv2023

Photonic stopband and reflectance asymmetry from thickness gradient in opals

The influence of thickness gradient and structural order on the spectral response of opal photonic crystals (PhCs) grown by evaporation-induced self-assembly (EISA) are presented. SEM imaging and angle resolved optical transmission spectroscopy are used to investigate the evolution of the PBG along a thickness gradient for opals grown from five different colloidal sphere concentrations at two different evaporation rates. The degradation of structural order along the thickness gradient is demonstrated, the occurrence of which attenuates the PBG with the thinning of the opal film and results in asymmetrical angle-resolved transmission spectra. The asymmetry in transmission intensity becomes more pronounced for opals grown from lower volume fractions, where secondary Bragg reflections also appear at low incident angles.

physics.optics↗
arXiv2023

Dispersion and Thickness Control in Evaporation-induced Self-Assembly of Opal Photonic Crystals

Opals are naturally occurring photonic crystals which can be formed easily using low-cost self-assembly methods. While the optical behaviour of opals has received significant attention over the last number of decades, there is limited information on the effect of crystal thickness on the optical properties they display. Here, the relationship between volume fraction and crystal thickness is established with an evaporation-induced self-assembly (EISA) method of formation. The extent to which thickness can be used to manipulate the optical properties of the crystals is explored, focusing on the change in the photonic band gap (PBG). Microscopical structural characterization and angle-resolved transmission spectroscopy are used to examine the quality of the photonic crystals formed using different volume fractions of polystyrene spheres, with thicknesses up to 37 layers grown from volume fractions of 0.125%. This work provides a direct correlation between sphere solution volume fraction and crystal thickness, and the associated optical fingerprint of opal photonic crystals. Maximum thickness is examined, which is shown to converge to a narrow range over several evaporation rates. We identify the criteria required to achieve thickness control in relatively fast evaporation induced self-assembly while maintaining structural quality, and the change to the spectroscopic signature to the (111) stopband and higher order (220) reflections, under conditions where a less ordered photonic crystals are formed.

physics.optics↗
arXiv2022

Operando Methods and Probes for Battery Electrodes and Materials

With the importance of Li-ion and emerging alternative batteries to our electric future, predicting new sustainable materials, electrolytes and complete cells that safely provide high performance, long life, energy dense capability is critically important. Understanding interface, microstructure of materials, the nature of electrolytes and factors that affect or limit long term performance are key to new battery chemistries, cell form factors and alternative materials. The electrochemical processes which cause these changes are also difficult to probe because of their metastability and lifetimes, which can be of nanosecond to sub nanosecond time domains. Consequently, developing and adapting high-resolution, non-destructive methods to capture these processes proves challenging, requiring state-of-the-art techniques.Recent progress is very promising, where optical spectroscopies, synchrotron radiation techniques, and energy-specific atom probe tomography and microscopy methods are just some of the approaches that are unravelling the true internal behaviour of battery cells in real-time.In this review, we overview many of the most promising non-destructive methods developed in recent years to assess battery material properties, interfaces, processes,and reactions under operando conditions in electrodes and full cells.

cond-mat.mtrl-sci↗
arXiv2017

A Minimal Set of Shannon-type Inequalities for Functional Dependence Structures

The minimal set of Shannon-type inequalities (referred to as elemental inequalities), plays a central role in determining whether a given inequality is Shannon-type. Often, there arises a situation where one needs to check whether a given inequality is a constrained Shannon-type inequality. Another important application of elemental inequalities is to formulate and compute the Shannon outer bound for multi-source multi-sink network coding capacity. Under this formulation, it is the region of feasible source rates subject to the elemental inequalities and network coding constraints that is of interest. Hence it is of fundamental interest to identify the redundancies induced amongst elemental inequalities when given a set of functional dependence constraints. In this paper, we characterize a minimal set of Shannon-type inequalities when functional dependence constraints are present.

cs.IT↗
arXiv2016

Capacity Bounds for Networks with Correlated Sources and Characterisation of Distributions by Entropies

Characterising the capacity region for a network can be extremely difficult. Even with independent sources, determining the capacity region can be as hard as the open problem of characterising all information inequalities. The majority of computable outer bounds in the literature are relaxations of the Linear Programming bound which involves entropy functions of random variables related to the sources and link messages. When sources are not independent, the problem is even more complicated. Extension of Linear Programming bounds to networks with correlated sources is largely open. Source dependence is usually specified via a joint probability distribution, and one of the main challenges in extending linear program bounds is the difficulty (or impossibility) of characterising arbitrary dependencies via entropy functions. This paper tackles the problem by answering the question of how well entropy functions can characterise correlation among sources. We show that by using carefully chosen auxiliary random variables, the characterisation can be fairly "accurate" Using such auxiliary random variables we also give implicit and explicit outer bounds on the capacity of networks with correlated sources. The characterisation of correlation or joint distribution via Shannon entropy functions is also applicable to other information measures such as Renyi entropy and Tsallis entropy.

cs.IT↗
arXiv2016

Characterising Probability Distributions via Entropies

Characterising the capacity region for a network can be extremely difficult, especially when the sources are dependent. Most existing computable outer bounds are relaxations of the Linear Programming bound. One main challenge to extend linear program bounds to the case of correlated sources is the difficulty (or impossibility) of characterising arbitrary dependencies via entropy functions. This paper tackles the problem by addressing how to use entropy functions to characterise correlation among sources.

cs.IT↗
arXiv2015

Compression and Recovery of Distributed Random Signals

We consider the case when a set of spatially distributed sensors make local observations which are noisy versions of a signal of interest. Each sensor transmits compressed information about its measurements to the fusion center which should recover the original signal within a prescribed accuracy. Such an information processing relates to a wireless sensor network (WSN) scenario. The key problem is to find models of the sensors and fusion center so that they will be optimal in the sense of minimization of the associated error under a certain criterion, such as the mean square error (MSE). We determine the models from the technique which is a combination of the maximum block improvement (MBI) method and the generic Karhunen-Lo\`{e}ve transform (KLT). The resulting multi-compressor KLT-MBI algorithm is given in terms of pseudo-inverse matrices and, therefore, it is numerically stable and always exists. The proposed model provides compression, de-noising and reconstruction of distributed signals for the cases when known methods either are not applicable (because of singularity of associated matrices) or produce larger associated errors. Error analysis is provided.

cs.IT↗
arXiv2014

Finding a closest point in a lattice of Voronoi's first kind

We show that for those lattices of Voronoi's first kind with known obtuse superbasis, a closest lattice point can be computed in $O(n^4)$ operations where $n$ is the dimension of the lattice. To achieve this a series of relevant lattice vectors that converges to a closest lattice point is found. We show that the series converges after at most $n$ terms. Each vector in the series can be efficiently computed in $O(n^3)$ operations using an algorithm to compute a minimum cut in an undirected flow network.

cs.IT↗
arXiv2014

On the rank of random matrices over finite fields

A novel lower bound is introduced for the full rank probability of random finite field matrices, where a number of elements with known location are identically zero, and remaining elements are chosen independently of each other, uniformly over the field. The main ingredient is a result showing that constraining additional elements to be zero cannot result in a higher probability of full rank. The bound then follows by "zeroing" elements to produce a block-diagonal matrix, whose full rank probability can be computed exactly. The bound is shown to be at least as tight and can be strictly tighter than existing bounds.

cs.IT↗
arXiv2013

On the Capacity of Networks with Correlated Sources

Characterizing the capacity region for a network can be extremely difficult. Even with independent sources, determining the capacity region can be as hard as the open problem of characterizing all information inequalities. The majority of computable outer bounds in the literature are relaxations of the Linear Programming bound which involves entropy functions of random variables related to the sources and link messages. When sources are not independent, the problem is even more complicated. Extension of linear programming bounds to networks with correlated sources is largely open. Source dependence is usually specified via a joint probability distribution, and one of the main challenges in extending linear programming bounds is the difficulty (or impossibility) of characterizing arbitrary dependencies via entropy functions. This paper tackles the problem by answering the question of how well entropy functions can characterize correlation among sources. We show that by using carefully chosen auxiliary random variables, the characterization can be fairly "accurate".

cs.IT↗
arXiv2013

Cut-Set Bounds on Network Information Flow

Explicit characterization of the capacity region of communication networks is a long standing problem. While it is known that network coding can outperform routing and replication, the set of feasible rates is not known in general. Characterizing the network coding capacity region requires determination of the set of all entropic vectors. Furthermore, computing the explicitly known linear programming bound is infeasible in practice due to an exponential growth in complexity as a function of network size. This paper focuses on the fundamental problems of characterization and computation of outer bounds for networks with correlated sources. Starting from the known local functional dependencies induced by the communications network, we introduce the notion of irreducible sets, which characterize implied functional dependencies. We provide recursions for computation of all maximal irreducible sets. These sets act as information-theoretic bottlenecks, and provide an easily computable outer bound. We extend the notion of irreducible sets (and resulting outer bound) for networks with independent sources. We compare our bounds with existing bounds in the literature. We find that our new bounds are the best among the known graph theoretic bounds for networks with correlated sources and for networks with independent sources.

cs.IT↗
arXiv2012

Error Free Perfect Secrecy Systems

Shannon's fundamental bound for perfect secrecy says that the entropy of the secret message cannot be larger than the entropy of the secret key initially shared by the sender and the legitimate receiver. Massey gave an information theoretic proof of this result, however this proof does not require independence of the key and ciphertext. By further assuming independence, we obtain a tighter lower bound, namely that the key entropy is not less than the logarithm of the message sample size in any cipher achieving perfect secrecy, even if the source distribution is fixed. The same bound also applies to the entropy of the ciphertext. The bounds still hold if the secret message has been compressed before encryption. This paper also illustrates that the lower bound only gives the minimum size of the pre-shared secret key. When a cipher system is used multiple times, this is no longer a reasonable measure for the portion of key consumed in each round. Instead, this paper proposes and justifies a new measure for key consumption rate. The existence of a fundamental tradeoff between the expected key consumption and the number of channel uses for conveying a ciphertext is shown. Optimal and nearly optimal secure codes are designed.

cs.IT↗
arXiv2012

Network Coding Capacity Regions via Entropy Functions

In this paper, we use entropy functions to characterise the set of rate-capacity tuples achievable with either zero decoding error, or vanishing decoding error, for general network coding problems. We show that when sources are colocated, the outer bound obtained by Yeung, A First Course in Information Theory, Section 15.5 (2002) is tight and the sets of zero-error achievable and vanishing-error achievable rate-capacity tuples are the same. We also characterise the set of zero-error and vanishing-error achievable rate capacity tuples for network coding problems subject to linear encoding constraints, routing constraints (where some or all nodes can only perform routing) and secrecy constraints. Finally, we show that even for apparently simple networks, design of optimal codes may be difficult. In particular, we prove that for the incremental multicast problem and for the single-source secure network coding problem, characterisation of the achievable set is very hard and linear network codes may not be optimal.

cs.IT↗
arXiv2010

Lossy Broadcasting in Two-Way Relay Networks with Common Reconstructions

The broadcast phase (downlink transmission) of the two-way relay network is studied in the source coding and joint source-channel coding settings. The rates needed for reliable communication are characterised for a number of special cases including: small distortions, deterministic distortion measures, and jointly Gaussian sources with quadratic distortion measures. The broadcast problem is also studied with common-reconstruction decoding constraints, and the rates needed for reliable communication are characterised for all discrete memoryless sources and per-letter distortion measures.

cs.IT↗
arXiv2010

Multipath Parameter Estimation from OFDM Signals in Mobile Channels

We study multipath parameter estimation from orthogonal frequency division multiplex signals transmitted over doubly dispersive mobile radio channels. We are interested in cases where the transmission is long enough to suffer time selectivity, but short enough such that the time variation can be accurately modeled as depending only on per-tap linear phase variations due to Doppler effects. We therefore concentrate on the estimation of the complex gain, delay and Doppler offset of each tap of the multipath channel impulse response. We show that the frequency domain channel coefficients for an entire packet can be expressed as the superimposition of two-dimensional complex sinusoids. The maximum likelihood estimate requires solution of a multidimensional non-linear least squares problem, which is computationally infeasible in practice. We therefore propose a low complexity suboptimal solution based on iterative successive and parallel cancellation. First, initial delay/Doppler estimates are obtained via successive cancellation. These estimates are then refined using an iterative parallel cancellation procedure. We demonstrate via Monte Carlo simulations that the root mean squared error statistics of our estimator are very close to the Cramer-Rao lower bound of a single two-dimensional sinusoid in Gaussian noise.

cs.IT↗
arXiv2009

Existence of new inequalities for representable polymatroids

An Ingletonian polymatroid satisfies, in addition to the polymatroid axioms, the inequalities of Ingleton (Combin. Math. Appln., 1971). These inequalities are required for a polymatroid to be representable. It is has been an open question as to whether these inequalities are also sufficient. Representable polymatroids are of interest in their own right. They also have a strong connection to network coding. In particular, the problem of finding the linear network coding capacity region is equivalent to the characterization of all representable, entropic polymatroids. In this paper, we describe a new approach to adhere two polymatroids together to produce a new polymatroid. Using this approach, we can construct a polymatroid that is not inside the minimal closed and convex cone containing all representable polymatroids. This polymatroid is proved to satisfy not only the Ingleton inequalities, but also the recently reported inequalities of Dougherty, Freiling and Zeger. A direct consequence is that these inequalities are not sufficient to characterize representable polymatroids.

cs.IT↗
arXiv2009

Decoding Network Codes by Message Passing

In this paper, we show how to construct a factor graph from a network code. This provides a systematic framework for decoding using message passing algorithms. The proposed message passing decoder exploits knowledge of the underlying communications network topology to simplify decoding. For uniquely decodeable linear network codes on networks with error-free links, only the message supports (rather than the message values themselves) are required to be passed. This proposed simplified support message algorithm is an instance of the sum-product algorithm. Our message-passing framework provides a basis for the design of network codes and control of network topology with a view toward quantifiable complexity reduction in the sink terminals.

cs.IT↗