Opportunistic use of unused spectrum could efficiently be carried out using the paradigm of Cognitive Radio (CR). A spectrum remains idle when the primary user (licensee) is not using it. The secondary nodes detect this spectral hole quickly and make use of it for data transmission during this interval and stop transmitting once the primary starts transmitting. Detection of spectral holes by the secondary is called spectrum sensing in the CR scenario. Spectrum Sensing is formulated as a hypothesis testing problem wherein under H0 the spectrum is free and under H1, occupied. The samples will have different probability distributions, P0 and P1, under H0 and H1 respectively. In the first part of the thesis, a new algorithm - entropy test is presented, which performs better than the available algorithms when P0 is known but not P1. This is extended to a distributed setting as well, in which different secondary nodes collect samples independently and send their decisions to a Fusion Centre (FC) over a noisy MAC which then makes the final decision. The asymptotic optimality of the algorithm is also shown. In the second part, the spectrum sensing problem under impediments such as fading, electromagnetic interference and outliers is tackled. Here the detector does not possess full knowledge of either P0 or P1. This is a more general and practically relevant setting. It is found that a recently developed algorithm (which we call random walk test) under suitable modifications works well. The performance of the algorithm theoretically and via simulations is shown. The same algorithm is extended to the distributed setting as above.

With the rapid increase in available compute power and memory, and bolstered by the advent of efficient formulations and algorithms, the role of 3D full-wave computational methods for accurate modelling of complex electromagnetic (EM) structures has gained in significance. The range of problems includes Radar Cross Section (RCS) computation, analysis and design of antennas and passive microwave circuits, bio-medical non-invasive detection and therapeutics, energy harvesting etc. Further, with the rapid advances in technology trends like System-in-Package (SiP) and System-on-Chip (SoC), the fidelity of chip-to-chip communication and package-board electrical performance parameters like signal integrity (SI), power integrity (PI), electromagnetic interference (EMI) are becoming increasingly critical. Rising pin-counts to satisfy functionality requirements and decreasing layer-counts to maintain cost-effectiveness necessitates 3D full wave electromagnetic solution for accurate system modelling. Method of Moments (MoM) is one such widely used computational technique to solve a 3D electromagnetic problem with full-wave accuracy. Due to lesser number of mesh elements or discretization on the geometry, MoM has an advantage of a smaller matrix size. However, due to Green's Function interactions, the MoM matrix is dense and its solution presents a time and memory challenge. The thesis focuses on formulation and development of novel techniques that aid in fast MoM based electromagnetic solutions. With the recent paradigm shift in computer hardware architectures transitioning from single-core microprocessors to multi-core systems, it is of prime importance to parallelize the serial electromagnetic formulations in order to leverage maximum computational benefits. Therefore, the thesis explores the possibilities to expedite an electromagnetic simulation by scalable parallelization of near-linear complexity algorithms like Fast Multipole Method (FMM) on a multi-core platform. Secondly, with the best of parallelization strategies in place and near-linear complexity algorithms in use, the solution time of a complex EM problem can still be exceedingly large due to over-meshing of the geometry to achieve a desired level of accuracy. Hence, the thesis focuses on judicious placement of mesh elements on the geometry to capture the physics of the problem without compromising on accuracy- a technique called Adaptive Mesh Refinement. This facilitates a reduction in the number of solution variables or degrees of freedom in the system and hence the solution time. For multi-scale structures as encountered in chip-package-board systems, the MoM formulation breaks down for parts of the geometry having dimensions much smaller as compared to the operating wavelength. This phenomenon is popularly known as low-frequency breakdown or low-frequency instability. It results in an ill-conditioned MoM system matrix, and hence higher iteration count to converge when solved using an iterative solver framework. This consequently increases the solution time of simulation. The thesis thus proposes novel formulations to improve the spectral properties of the system matrix for real-world complex conductor and dielectric structures and hence form well-conditioned systems. This reduces the iteration count considerably for convergence and thus results in faster solution. Finally, minor changes in the geometrical design layouts can adversely affect the time-to-market of a commodity or a product. This is because the intermediate design variants, in spite of having similarities between them are treated as separate entities and therefore have to follow the conventional model-mesh-solve workflow for their analysis. This is a missed opportunity especially for design variant problems involving near-identical characteristics when the information from the previous design variant could have been used to expedite the simulation of the present design iteration. A similar problem occurs in the broadband simulation of an electromagnetic structure. The solution at a particular frequency can be expedited manifold if the matrix information from a frequency in its neighbourhood is used, provided the electrical characteristics remain nearly similar. The thesis introduces methods to re-use the subspace or Eigen-space information of a matrix from a previous design or frequency to solve the next incremental problem faster.

There is an ever increasing demand for higher spectral usage in wireless communication, radar and imaging systems. Higher spectral efficiency can be achieved using components that are aware of system environment and adapt suitably to the operating conditions. In this regard, radio frequency (RF) signal analysis is of paramount interest. Emergence of dispersive delay networks (DDN) has led to the significant development of microwave analogue-signal processing (ASP) and analysis. DDN causes displacement of spectral components in time domain, relative to the frequency dependant group delay response. The main challenge in the design of DDN in this context is in achieving broad bandwidth with high group delay dispersion (GDD). In this regard, all-pass networks (APN) have been explored as a potential wide-band DDN owing to the possibility of controlling the magnitude of loss characteristics without affecting the dispersion in group delay response. The synthesis procedure of lumped element APN using approximation methods is well known at audio frequencies. Most of these use operational amplifier and cannot be extended directly to RF. There is no generalised closed form analytical procedure at RF for the synthesis of APN with the required GDD. In this regard, this dissertation presents the design and implementation of all-pass networks as wide-band dispersive delay networks at radio frequencies. In this work, we begin by analysing the signal propagation through a DDN with a linear group delay response over a broad bandwidth. It is found that the signal experiences expansion of pulse width, reduction of its peak amplitude and a temporal displacement of the spectral components. Analytical expressions derived help initial synthesis of group delay response required for various ASP applications. As the first step towards implementation at RF, a single stage APN is designed using surface mount devices (SMD). This design approach takes into account practical issues such as parasitic due to mounting pads, available component values, physical dimensions, self-resonance frequency (SRF) and finite Q factor of the components used. Full wave simulation of the design with transmission line pads and components is carried out. This implementation is useful for frequencies up to the component SRF, generally about 5 GHz. This design approach makes the circuit footprint independent of frequency and the performance is limited only by the Q factor of the adopted technology. The Q factor affects the loss characteristics with a negligible effect on group delay response in the frequency band of interest. In order to extend the APN design for high group delay, a novel board level implementation is developed consisting of both lumped SMD components and distributed elements. The implementation results in a lower sensitivity of group delay performance to the commercially specified component value tolerances than the approach using all SMD components. It has been experimentally verified that the measured group delay is 2.4 ns at 1.85 GHz, which is thrice that reported in other approaches. The implementation has a reduced circuit footprint and is attractive in practical applications as it is a single layer micro strip realisation with less complex fabrication procedure and fewer components to assemble. As an extension of this towards wideband cascaded APN, an iterative design procedure is developed to achieve a monotonous group delay response over a broad bandwidth. The approach facilitates cascading of multiple stages of lumped APN with different resonance frequency and peak group delay to obtain linear and non-linear group delay responses with both positive and negative GDD. Circuits with both positive and negative GDD are required for various ASP applications such as compressive receivers and the present approach is unique in obtaining both the responses, not possible with many other RF dispersion techniques. Circuit models have been simulated by cascading transfer function responses of the individual APNs. The design is further extended for SMD implementation. To validate the above approach, a two stage APN is designed in the frequency range [0.5 - 1] GHz for a linear GDD of ±6 ns/GHz. Two negative GDD APNs are further cascaded to obtain a four stage implementation with an overall GDD of -12 ns/GHz. The experimental results are compared with full wave simulations for validation. The design using lumped SMD components has greatly improved the performance in terms of GDD with a reduced circuit footprint and lower insertion loss than previously reported approaches. As practical examples, the ASP modules are experimentally demonstrated using the fabricated APN. Frequency discrimination of two input frequencies with a frequency resolution of 500 MHz is demonstrated. Higher GDD results in higher separation of frequency components in time domain. Pulse compression and magnification is also demonstrated for different wideband LFM input signals. The dispersion effects of amplitude reduction, pulse width expansion and frequency chirping are thereby validated experimentally. In summary, the approaches presented in this dissertation enable the design of wideband all-pass networks to introduce dispersion delays over wide bandwidths, opening up the possibility for their use in analogue signal processing at radio frequencies. Some of these applications have been experimentally demonstrated and validated using time frequency analysis.

Through the history of mankind, novel materials have played a key role in techno- logical progress. As we approach the limits of scaling it becomes difficult to squeeze out any more extensions to Moore’s law by just reducing device feature sizes. It is important to look for an alternate semiconductor to silicon in order to continue making the progress predicted by Moore’s law. Among the various semiconductor options being explored world-wide, the III-nitride semiconductor material system has certain unique characteristics that make it one of the leading contenders. We explore the III-nitride semiconductor material system for the unique advantages that it offers over the other alternatives available to us. This thesis studies the device applications of epitaxial III-nitride films and nanos- tructures grown using plasma assisted molecular beam epitaxy (PAMBE) The material characterisation of the PAMBE grown epitaxial III-nitrides was car- ried out using techniques like high resolution X-ray diffraction (HR-XRD), field emis- sion scanning electron microscopy (FESEM), room temperature photoluminescence (PL) and transmission electron microscopy (TEM). The epitaxial III-nitrides were then further processed to fabricate devices like Schottky diodes, photodetectors and surface acoustic wave (SAW) devices. The electrical charcterisation of the fabricated devices was carried out using techniques like Hall measurement, IV and CV measure- ments on a DC probe station and S-parameter measurements on a vector network analyser connected to an RF probe station. We begin our work on Schottky diodes by explaining the motivation for adding an interfacial layer in a metal-semiconductor Schottky contact and how high-k di- electrics like HfO2 have been relatively unexplored in this application. We report the work carried out on the Pt/n-GaN metal-semiconductor (MS) Schottky and the Pt/HfO2/n-GaN metal-insulator-semiconductor (MIS) Schottky diode. We report an improvement in the diode parameters like barrier height (0.52 eV to 0.63 eV), ideality factor (2.1 to 1.3) and rectification ratio (35.9 to 98.9 @2V bias) after the introduction of 5 nm of HfO2 as the interfacial layer. Temperature dependent I-V measurements were done to gain a further understanding of the interface. We observe that the barrier height and ideality factor exhibit a temperature dependence. This was attributed to inhomogeneities at the interface and by assuming a Gaussian distribution of barrier heights. UV and IR photodetectors using III-nitrides are then studied. Our work on UV photodetectors describes the growth of epitaxial GaN films. Au nanoparticles were fabricated on these films using thermal evaporation and annealing. Al nanostruc- tures were fabricated using nanosphere lithography. Plasmonic enhancement using these metallic nanostructures was explored by fabricating metal-semiconductor-metal (MSM) photodetectors. We observed plasmonic enhancement of photocurrent in both cases. To obtain greater improvement, we etched down on the GaN film using reac tive ion etching (RIE). This resulted in further increase in photocurrent along with a reduction in dark current which was attributed to creation of new trap states. IR photodetectors studied in this thesis are InN quantum dots whose density can be controlled by varying the indium flux during growth. We observe that increase in InN quantum dot density results in increase in photocurrent and decrease in dark current in the fabricated IR photodetectors. We then explore the advantages that InGaN offers as a material that supports surface acoustic waves and fabricate InGaN based surface acoustic wave devices. We describe the growth of epitaxial In0.23 Ga0.77 N films on GaN template using molecular beam epitaxy. Material characterisation was carried out using HR-XRD, FESEM, PL and TEM. The composition was determined from HR-XRD and PL measurements and both results matched each other. This was followed by the fabrication of interdigited electrodes with finger spacing of 10 µm. S-parameter results showed a transmission peak at 104 MHz with an insertion loss of 19 dB. To the best of our knowledge, this is the first demonstration of an InGaN based SAW device. In summary, this thesis demonstrates the practical advantages of epitaxially grown film and nanostructured III-nitride materials such as GaN, InN and InGaN using plasma assisted molecular beam epitaxy for Schottky diodes, UV and IR photodetec- tors and surface acoustic wave devices.

Software Defined Radios (SDRs) and Cognitive Radios (CRs) pave the way for next-generation radio technology. They promise versatility, flexibility and cognition which can revolutionize communications systems. However they present greater challenges to the design of radio frequency (RF) front-ends. RF front-ends for the radios in use today are narrow-band in their frequency response and are optimized and tuned to the carrier frequency of interest. SDRs and CRs demand front-ends which are versatile, configurable, tunable and be capable of transmitting and receiving signals with different bandwidths and modulation schemes. Integrating power amplifiers (PAs) with transmitters in CMOS has many advantages and challenges. This thesis deals with the design of an RF transmitter front-end for SDRs and CRs in CMOS. The thesis begins with an introduction to SDRs and the requirements they place on transmitters and the challenges involved in designing them in CMOS. After a brief overview of the existing techniques, the proposed architecture is presented and explained. A digitally intensive transmitter solution is proposed. The transmitter covers a wide frequency range of 750 MHz to 2.5 GHz. The inputs to the proposed transmitter are in-phase and quadrature (I & Q) data bit streams. Multiple stages of up-sampling and filtering are used to remove all spurs in the spectrum such that only the harmonics of the carrier remain. Differential rail-to-rail quadrature clocks are generated from a continuous wave signal at twice the carrier frequency. The clocks are corrected for their duty cycle and quadrature impairments. The heart of the transmitter is an integrated reconfigurable CMOS power amplifier (PA). A methodology to design reconfigurable Class E PAs with a series fixed inductor has been presented. A CMOS power amplifier that can span a wide frequency range with sufficient output power and efficiency, supporting varying envelope complex modulation signals, with good linearity has been designed. Digital pre-distortion (DPD) is used to linearize the PA. The full transmitter and the clock correction blocks have been designed and fabricated in a commercial 130-nm CMOS process and experimentally characterized. The PA delivers a maximum power of 13 dBm with an efficiency of 27% at 1 GHz. While transmitting a 16-QAM signal at 1 GHz, the measured EVM is 4%. It delivers a maximum power of around 11-13 dBm from 750 MHz to 1.5 GHz and up to 6.5 dBm of power till 2.5 GHz. Comparing the proposed system with recently published literature, it can be seen that the proposed design is one of the very few transmitters which has an integrated matching network, tunable across the frequency range. The proposed PA produces the highest output power and with largest efficiency for systems with on-chip output networks.

In this work, we study two problems in information-theoretic security. Firstly, we study a wireless network where two nodes want to securely exchange messages via an honest-but-curious bidirectional relay. There is no direct link between the user nodes, and all communication must take place through the relay. The relay behaves like a passive eavesdropper, but otherwise follows the protocol it is assigned. Our objective is to design a scheme where the user nodes can reliably exchange messages such that the relay gets no information about the individual messages. We first describe a perfectly secure scheme using nested lattices, and show that our scheme achieves secrecy regardless of the distribution of the additive noise, and even if this distribution is unknown to the user nodes. Our scheme is explicit, in the sense that for any pair of nested lattices, we give the distribution used for randomization at the encoders to guarantee security. We then give a strongly secure lattice coding scheme, and we characterize the performance of both these schemes in the presence of Gaussian noise. We then extend our perfectly-secure and strongly-secure schemes to obtain a protocol that guarantees end-to-end secrecy in a multichip line network. We also briefly study the robustness of our bidirectional relaying schemes to channel imperfections. In the second problem, we consider the scenario where multiple terminals have access to private correlated Gaussian sources and a public noiseless communication channel. The objective is to generate a group secret key using their sources and public communication in a way that an eavesdropper having access to the public communication can obtain no information about the key. We give a nested lattice-based protocol for generating strongly secure secret keys from independent and identically distributed copies of the correlated random variables. Under certain assumptions on the joint distribution of the sources, we derive achievable secret key rates. The tools used in designing protocols for both these problems are nested lattice codes, which have been widely used in several problems of communication and security. In this thesis, we also study lattice constructions that permit polynomial-time encoding and decoding. In this regard, we first look at a class of lattices obtained from low-density parity-check (LDPC) codes, called Low-density Construction-A (LDA) lattices. We show that high-dimensional LDA lattices have several “goodness” properties that are desirable in many problems of communication and security. We also present a new class of low-complexity lattice coding schemes that achieve the capacity of the AWGN channel. Codes in this class are obtained by concatenating an inner Construction-A lattice code with an outer Reed-Solomon code or an expander code. We show that this class of codes can achieve the capacity of the AWGN channel with polynomial encoding and decoding complexities. Furthermore, the probability of error decays exponentially in the block length for a fixed transmission rate R that is strictly less than the capacity. To the best of our knowledge, this is the first capacity-achieving coding scheme for the AWGN channel which has an exponentially decaying probability of error and polynomial encoding/decoding complexities.

High resolution surveillance video cameras are invaluable resources for effective crime prevention and forensic investigations. However, increasing communication bandwidth requirements of high definition surveillance videos are severely limiting the number of cameras that can be deployed. Higher bitrate also increases operating expenses due to higher data communication and storage costs. Hence, it is essential to develop low complexity algorithms which reduce data rate of the compressed video stream without affecting the image fidelity. In this thesis, a computer vision aided H.264 surveillance video encoder and four associated algorithms are proposed to reduce the bitrate. The proposed techniques are (I) Speeded up foreground segmentation, (II) Skip decision, (III) Reference frame selection and (IV) Face Region-of-Interest (ROI) coding. In the first part of the thesis, a modification to the adaptive Gaussian Mixture Model (GMM) based foreground segmentation algorithm is proposed to reduce computational complexity. This is achieved by replacing expensive floating point computations with low cost integer operations. To maintain accuracy, we compute periodic floating point updates for the GMM weight parameter using the value of an integer counter. Experiments show speedups in the range of 1.33 - 1.44 on standard video datasets where a large fraction of pixels are multimodal. In the second part, we propose a skip decision technique that uses a spatial sampler to sample pixels. The sampled pixels are segmented using the speeded up GMM algorithm. The storage pattern of the GMM parameters in memory is also modified to improve cache performance. Skip selection is performed using the segmentation results of the sampled pixels. In the third part, a reference frame selection algorithm is proposed to maximize the number of background Macroblocks (MB’s) (i.e. MB’s that contain background image content) in the Decoded Picture Buffer. This reduces the cost of coding uncovered background regions. Distortion over foreground pixels is measured to quantify the performance of skip decision and reference frame selection techniques. Experimental results show bit rate savings of up to 94.5% over methods proposed in literature on video surveillance data sets. The proposed techniques also provide up to 74.5% reduction in compression complexity without increasing the distortion over the foreground regions in the video sequence. In the final part of the thesis, face and shadow region detection is combined with the skip decision algorithm to perform ROI coding for pedestrian surveillance videos. Since person identification requires high quality face images, MB’s containing face image content are encoded with a low Quantization Parameter setting (i.e. high quality). Other regions of the body in the image are considered as RORI (Regions of reduced interest) and are encoded at low quality. The shadow regions are marked as Skip. Techniques that use only facial features to detect faces (e.g. Viola Jones face detector) are not robust in real world scenarios. Hence, we propose to initially detect pedestrians using deformable part models. The face region is determined using the deformed part locations. Detected pedestrians are tracked using an optical flow based tracker combined with a Kalman filter. The tracker improves the accuracy and also avoids the need to run the object detector on already detected pedestrians. Shadow and skin detector scores are computed over super pixels. Bilattice based logic inference is used to combine multiple likelihood scores and classify the super pixels as ROI, RORI or RONI. The coding mode and QP values of the MB’s are determined using the super pixel labels. The proposed techniques provide a further reduction in bitrate of up to 50.2%.

This thesis proposes and analyzes data fusion algorithms that operate on the physical layer of a wireless sensor network, in the context of three applications of cognitive radios: 1. Cooperative spectrum sensing via binary consensus; 2. Multiple transmitter localization and communication footprint identification; 3.Target self-localization using beacon nodes. For the first application, a co-phasing based data combining scheme is studied under imperfect channel knowledge. The evolution of network consensus state is modeled as a Markov chain, and the average transition probability matrix is derived. Using this, the average hitting time and average consensus duration are obtained, which are used to determine and optimize the performance of the consensus procedure. Second, using the fact that a typical communication footprint map admits a sparse representation, two novel compressed sensing based schemes are proposed to construct the map using 1-bit decisions from sensors deployed in a geographical area. The number of transmitters is determined using the K-means algorithm and a circular fitting technique, and a design procedure is proposed to determine the power thresholds for signal detection at sensors. Third, an algorithm is proposed for self-localization of a target node using power measurements from beacon nodes transmitting from known locations. The geographical area is overlaid with a virtual grid, and the problem is treated as one of testing overlapping subsets of grid cells for the presence of the target node. The column matching algorithm from group testing literature is considered for devising the target localization algorithm. The average probability of localizing the target within a grid cell is derived using the tools from Poisson point processes and order statistics. This quantity is used to determine the minimum required node density to localize the target within a grid cell with high probability. The performance of all the proposed algorithms is illustrated through Monte Carlo simulations.

In wireless communication systems, the use of multiple antennas, also known as Multiple-Input Multiple-Output(MIMO) communications, is now a widely accepted and important technology for improving their reliability and throughput performance. However, in order to achieve the performance gains predicted by the theory, the transmitter and receiver need to have accurate and up-to-date Channel State Information(CSI) to overcome the vagaries of the fading environment. Traditionally, the CSI is obtained at the receiver by sending a known training sequence in the forward-link direction. This CSI has to be conveyed to the transmitter via a low-rate, low latency and noisy feedback channel in the reverse-link direction. This thesis addresses three key challenges in sending the CSI to the transmitter of a MIMO communication system over the reverse-link channel, and provides novel solutions to them. The first issue is that the available CSI at the receiver has to be quantized to a finite number of bits, sent over a noisy feedback channel, reconstructed at the transmitter, and used by the transmitter for precoding its data symbols. In particular, the CSI quantization technique has to be resilient to errors introduced by the noisy reverse-link channel, and it is of interest to design computationally simple, linear filters to mitigate these errors. The second issue addressed is the design of low latency and low decoding complexity error correction codes to provide protection against fading conditions and noise in the reverse-link channel. The third issue is to improve the resilience of the reverse-link channel to fading. The solution to the first problem is obtained by proposing two classes of receive filtering techniques, where the output of the source decoder is passed through a filter designed to reduce the overall distortion including the effect of the channel noise. This work combines the high resolution quantization theory and the optimal Minimum Mean Square Error(MMSE) filtering formulation to analyze, and optimize, the total end-to-end distortion. As a result, analytical expressions for the linear receive filters are obtained that minimize the total end-to-end distortion, given the quantization scheme and source(channel state) distribution. The solution to the second problem is obtained by proposing a new family of error correction codes, termed trellis coded block codes, where a trellis code and block code are concatenated in order to provide good coding gain as well as low latency and low complexity decoding. This code construction is made possible due to the existence of a uniform partitioning of linear block codes. The solution to the third problem is obtained by proposing three novel transmit precoding methods that are applicable to time-division-duplex systems, where the channel reciprocity can be exploited in designing the precoding scheme. The proposed precoding methods convert the Rayleigh fading MIMO channel into parallel Additive White Gaussian Noise(AWGN) channels with fixed gain, while satisfying an average transmit power constraint. Moreover, the receiver does not need to have knowledge of the CSI in order to decode the received data. These precoding methods are also extended to Rayleigh fading multi-user MIMO channels. Finally, all the above methods are applied to the problem of designing a low-rate, low-latency code for the noisy and fading reverse-link channel that is used for sending the CSI. Simulation results are provided to demonstrate the improvement in the forward-link data rate due to the proposed methods. Note that, although the three solutions are presented in the context of CSI feedback in MIMO communications, their development is fairly general in nature, and, consequently, the solutions are potentially applicable in other communication systems also.

The classical binary error correcting codes, and subspace codes for error correction in random network coding are two different forms of error control coding. We identify common features between these two forms and study the relations between them using the aid of lattices. Lattices are partial ordered sets where every pair of elements has a least upper bound and a greatest lower bound in the lattice. We shall demonstrate that many questions that connect these forms have a natural motivation from the viewpoint of lattices. We shall show that a lattice framework captures the notion of Singleton bound where the bound is on the size of the code as a function of its parameters. For the most part, we consider a special type of a lattice which has the geometric modular property. We will use a lattice framework to combine the two different forms. And then, in order to demonstrate the utility of this binding view, we shall derive a general version of Singleton bound. We will note that the Singleton bounds behave differently in certain respects because the binary coding framework is associated with a lattice that is distributive. We shall demonstrate that lack of distributive gives rise to a weaker bound. We show that Singleton bound for classical binary codes, subspace codes, rank metric codes and Ferrers diagram rank metric codes can be derived using a common technique. In the literature, Singleton bounds are derived for Ferrers diagram rank metric codes where the rank metric codes are linear. We introduce a generalized version of Ferrers diagram rank metric codes and obtain a Singleton bound for this version. Next, we shall prove a conjecture concerning the constraints of embedding a binary coding framework into a subspace framework. We shall prove a conjecture by Braun, Etzion and Vardy, which states that any such embedding which contains the full space in its range is constrained to have a particular size. Our proof will use a theorem due to Lovasz, a subspace counting theorem for geometric modular lattices, to prove the conjecture. We shall further demonstrate that any code that achieves the conjectured size must be of a particular type. This particular type turns out to be a natural distributive sub-lattice of a given geometric modular lattice.