Due to the sheer volume of data involved, video coding is an important application of lossy source coding, and has received wide industrial interest and support as evidenced by the development and success of a series of video coding standards. All MPEG-series and H-series video coding standards proposed so far are based upon a video coding paradigm called predictive video coding, where video source frames Xᵢ,i=1,2,...,N, are encoded in a frame by frame manner, the encoder and decoder for each frame Xᵢ, i =1, 2, ..., N, enlist help only from all previous encoded frames Sj, j=1, 2, ..., i-1. In this thesis, we will look further beyond all existing and proposed video coding standards, and introduce a new coding paradigm called causal video coding, in which the encoder for each frame Xᵢ can use all previous original frames Xj, j=1, 2, ..., i-1, and all previous encoded frames Sj, while the corresponding decoder can use only all previous encoded frames. We consider all studies, comparisons, and designs on causal video coding from an information theoretic point of view. Let R*c(D₁,...,D_N) (R*p(D₁,...,D_N), respectively) denote the minimum total rate required to achieve a given distortion level D₁,...,D_N > 0 in causal video coding (predictive video coding, respectively). A novel computation approach is proposed to analytically characterize, numerically compute, and compare the minimum total rate of causal video coding R*c(D₁,...,D_N) required to achieve a given distortion (quality) level D₁,...,D_N > 0. Specifically, we first show that for jointly stationary and ergodic sources X₁, ..., X_N, R*c(D₁,...,D_N) is equal to the infimum of the n-th order total rate distortion function R_{c,n}(D₁,...,D_N) over all n, where R_{c,n}(D₁,...,D_N) itself is given by the minimum of an information quantity over a set of auxiliary random variables. We then present an iterative algorithm for computing R_{c,n}(D₁,...,D_N) and demonstrate the convergence of the algorithm to the global minimum. The global convergence of the algorithm further enables us to not only establish a single-letter characterization of R*c(D₁,...,D_N) in a novel way when the N sources are an independent and identically distributed (IID) vector source, but also demonstrate a somewhat surprising result (dubbed the more and less coding theorem)---under some conditions on source frames and distortion, the more frames need to be encoded and transmitted, the less amount of data after encoding has to be actually sent. With the help of the algorithm, it is also shown by example that R*c(D₁,...,D_N) is in general much smaller than the total rate offered by the traditional greedy coding method by which each frame is encoded in a local optimum manner based on all information available to the encoder of the frame. As a by-product, an extended Markov lemma is established for correlated ergodic sources. From an information theoretic point of view, it is interesting to compare causal video coding and predictive video coding, which all existing video coding standards proposed so far are based upon. In this thesis, by fixing N=3, we first derive a single-letter characterization of R*p(D₁,D₂,D₃) for an IID vector source (X₁,X₂,X₃) where X₁ and X₂ are independent, and then demonstrate the existence of such X₁,X₂,X₃ for which R*p(D₁,D₂,D₃)>R*c(D₁,D₂,D₃) under some conditions on source frames and distortion. This result makes causal video coding an attractive framework for future video coding systems and standards. The design of causal video coding is also considered in the thesis from an information theoretic perspective by modeling each frame as a stationary information source. We first put forth a concept called causal scalar quantization, and then propose an algorithm for designing optimum fixed-rate causal scalar quantizers for causal video coding to minimize the total distortion among all sources. Simulation results show that in comparison with fixed-rate predictive scalar quantization, fixed-rate causal scalar quantization offers as large as 16% quality improvement (distortion reduction).

Research Doctorate - Doctor of Philosophy (PhD) / This thesis presents results on optimal coding and decoding of discrete-time stochastic signals, in the sense of minimizing a distortion metric subject to a constraint on the bit-rate and on the signal transfer function from source to reconstruction. The first (preliminary) contribution of this thesis is the introduction of new distortion metric that extends the mean squared error (MSE) criterion. We give this extension the name Weighted-Correlation MSE (WCMSE), and use it as the distortion metric throughout the thesis. The WCMSE is a weighted sum of two components of the MSE: the variance of the error component uncorrelated to the source, on the one hand, and the remainder of the MSE, on the other. The WCMSE can take account of signal transfer function constraints by assigning a larger weight to deviations from a target signal transfer function than to source-uncorrelated distortion. Within this framework, the second contribution is the solution of a family of feedback quantizer design problems for wide sense stationary sources using an additive noise model for quantization errors. These associated problems consist of finding the frequency response of the filters deployed around a scalar quantizer that minimize the WCMSE for a fixed quantizer signal-to-(granular)-noise ratio (SNR). This general structure, which incorporates pre-, post-, and feedback filters, includes as special cases well known source coding schemes such as pulse coded modulation (PCM), Differential Pulse-Coded Modulation (DPCM), Sigma Delta converters, and noise-shaping coders. The optimal frequency response of each of the filters in this architecture is found for each possible subset of the remaining filters being given and fixed. These results are then applied to oversampled feedback quantization. In particular, it is shown that, within the linear model used, and for a fixed quantizer SNR, the MSE decays exponentially with oversampling ratio, provided optimal filters are used at each oversampling ratio. If a subtractively dithered quantizer is utilized, then the noise model is exact, and the SNR constraint can be directly related to the bit-rate if entropy coding is used, regardless of the number of quantization levels. On the other hand, in the case of fixed-rate quantization, the SNR is related to the number of quantization levels, and hence to the bit-rate, when overload errors are negligible. It is shown that, for sources with unbounded support, the latter condition is violated for sufficiently large oversampling ratios. By deriving an upper bound on the contribution of overload errors to the total WCMSE, a lower bound for the decay rate of the WCMSE as a function of the oversampling ratio is found for fixed-rate quantization of sources with finite or infinite support. The third main contribution of the thesis is the introduction of the rate-distortion function (RDF) when WCMSE is the distortion metric, denoted by WCMSE-RDF. We provide a complete characterization for Gaussian sources. The resulting WCMSE-RDF yields, as special cases, Shannon's RDF, as well as the recently introduced RDF for source-uncorrelated distortions (RDF-SUD). For cases where only source-uncorrelated distortion is allowed, the RDF-SUD is extended to include the possibility of linear-time invariant feedback between reconstructed signal and coder input. It is also shown that feedback quantization schemes can achieve a bit-rate only 0.254 bits/sample above this RDF by using the same filters that minimize the reconstruction MSE for a quantizer-SNR constraint. The fourth main contribution of this thesis is to provide a set of conditions under which knowledge of a realization of the RDF can be used directly to solve encoder-decoder design optimization problems. This result has direct implications in the design of subband coders with feedback, as well as in the design of encoder-decoder pairs for applications such as networked control. As the fifth main contribution of this thesis, the RDF-SUD is utilized to show that, for Gaussian sta-tionary sources with memory and MSE distortion criterion, an upper bound on the information-theoretic causal RDF can be obtained by means of an iterative numerical procedure, at all rates. This bound is tighter than 0:5 bits/sample. Moreover, if there exists a realization of the causal RDF in which the re-construction error is jointly stationary with the source, then the bound obtained coincides with the causal RDF. The iterative procedure proposed here to obtain Ritc(D) also yields a characterization of the filters in a scalar feedback quantizer having an operational rate that exceeds the bound by less than 0:254 bits/sample. This constitutes an upper bound on the optimal performance theoretically attainable by any causal source coder for stationary Gaussian sources under the MSE distortion criterion.

Abstract Wireless sensor networks (WSNs) consisting of battery-powered sensors are increasingly deployed for a myriad of Internet of Things applications, e.g., environmental, industrial, and healthcare monitoring. Since wireless access is typically the main contributor to battery usage, minimizing communications is crucial to prolong network lifetime and improve user experience. The objective of this thesis is to develop and analyze energy-efficient distributed compressed data acquisition techniques for WSNs. The thesis proposes four approaches to conserve sensors' energy by minimizing the amount of information each sensor has to transmit to meet given application requirements. The first part addresses a cross-layer design to minimize the sensors’ sum transmit power via joint optimization of resource allocation and multi-path routing. A distributed consensus optimization based algorithm is proposed to solve the problem. The algorithm is shown to have superior convergence compared to several baselines. The remaining parts deal with compressed sensing (CS) of sparse/compressible sources. The second part focuses on the distributed CS acquisition of spatially and temporally correlated sensor data streams. A CS algorithm based on sliding window and recursive decoding is developed. The method is shown to achieve higher reconstruction accuracy with fewer transmissions and less decoding delay and complexity compared to several baselines, and to progressively refine past estimates. The last two approaches incorporate the quantization of CS measurements and focus on lossy source coding. The third part addresses the distributed quantized CS (QCS) acquisition of correlated sparse sources. A distortion-rate optimized variable-rate QCS method is proposed. The method is shown to achieve higher distortion-rate performance than the baselines and to enable a trade-off between compression performance and encoding complexity via the pre-quantization of measurements. The fourth part investigates information-theoretic rate-distortion (RD) performance limits of single-sensor QCS. A lower bound to the best achievable compression — defined by the remote RD function (RDF) — is derived. A method to numerically approximate the remote RDF is proposed. The results compare practical QCS methods to the derived limits, and show a novel QCS method to approach the remote RDF. / Tiivistelmä Patterikäyttöisistä antureista koostuvat langattomat anturiverkot yleistyvät esineiden internetin myötä esim. ympäristö-, teollisuus-, ja terveydenhoitosovelluksissa. Koska langaton tiedonsiirto kuluttaa merkittävästi energiaa, kommunikoinnin minimointi on elintärkeää pidentämään verkon elinikää ja parantamaan käyttäjäkokemusta. Väitöskirjan tavoitteena on kehittää ja analysoida energiatehokkaita hajautettuja pakattuja datankeruumenetelmiä langattomiin anturiverkkoihin. Työssä ehdotetaan neljä lähestymistapaa, jotka säästävät anturien energiaa minimoimalla se tiedonsiirron määrä, mikä vaaditaan täyttämään sovelluksen asettamat kriteerit. Väitöskirjan ensimmäinen osa tarkastelee protokollakerrosten yhteissuunnittelua, jossa minimoidaan anturien yhteislähetysteho optimoimalla resurssiallokaatio ja monitiereititys. Ratkaisuksi ehdotetaan konsensukseen perustuva hajautettu algoritmi. Tulokset osoittavat algoritmin suppenemisominaisuuksien olevan verrokkejaan paremmat. Loppuosat keskittyvät harvojen lähteiden pakattuun havaintaan (compressed sensing, CS). Toinen osa keskittyy tila- ja aikatasossa korreloituneen anturidatan hajautettuun keräämiseen. Työssä kehitetään liukuvaan ikkunaan ja rekursiiviseen dekoodaukseen perustuva CS-algoritmi. Tulokset osoittavat menetelmän saavuttavan verrokkejaan korkeamman rekonstruktiotarkkuuden pienemmällä tiedonsiirrolla sekä dekoodausviiveellä ja -kompleksisuudella ja kykenevän asteittain parantamaan menneitä estimaatteja. Työn viimeiset osat sisällyttävät järjestelmämalliin CS-mittausten kvantisoinnin keskittyen häviölliseen lähdekoodaukseen. Kolmas osa käsittelee hajautettua korreloitujen harvojen signaalien kvantisoitua CS-havaintaa (quantized CS, QCS). Työssä ehdotetaan särön ja muuttuvan koodinopeuden välisen suhteen optimoiva QCS-menetelmä. Menetelmällä osoitetaan olevan verrokkejaan parempi pakkaustehokkuus sekä kyky painottaa suorituskyvyn ja enkooderin kompleksisuuden välillä mittausten esikvantisointia käyttäen. Neljäs osa tutkii informaatioteoreettisia, koodisuhde-särösuhteeseen perustuvia suorituskykyrajoja yhden anturin QCS-järjestelmässä. Parhaimmalle mahdolliselle pakkaustehokkuudelle johdetaan alaraja, sekä kehitetään menetelmä sen numeeriseen arviointiin. Tulokset vertaavat käytännön QCS-menetelmiä johdettuihin rajoihin, ja osoittavat ehdotetun QCS-menetelmän saavuttavan lähes optimaalinen suorituskyky.