<p>In this thesis we study the complexity of data recovery from synchronization errors, namely insertion and deletion (insdel) errors.</p> <p>Insdel Locally Decodable Codes (Insdel LDCs) are error-correcting codes that admit super-efficient decoding algorithms even in the presence of many insdel errors. The study of such codes for Hamming errors have spanned several decades, whereas work on the insdel analogue had amounted to only a few papers before our work. This work initiates a systematic study of insdel LDCs, seeking to bridge this gap through designing codes and proving limitations. Our upper bounds essentially match those for Hamming LDCs in important ranges of parameters, even though insdel LDCs are more general than Hamming LDCs. Our main results are lower bounds that are exponentially stronger than the ones inherited from the Hamming LDCs. These results also have implications for the well-studied variant of relaxed LDCs. For this variant, besides showing the first results in the insdel setting, we also answer an open question for the Hamming variant by showing a strong lower bound.</p> <p>In the trace reconstruction problem, the goal is to recover an unknown source string x \in {0,1}n from random traces, which are obtained by hitting the source string with random deletion/insertions at a fixed rate. Mean-based algorithms are a class of reconstruction algorithms whose outputs depend only on the empirical estimates of individual bits. The number of traces needed for mean-based trace reconstruction has already been settled. We further study the performance of mean-based algorithms in a scenario where one wants to distinguish between two source strings parameterized by their edit distance, and we also provide explicit construction of strings that are hard to distinguish. We further establish an equivalence to the Prouhet-Tarry-Escott problem from number theory, which ends up being an obstacle to constructing explicit hard instances against mean-based algorithms.</p>

Time synchronization is critical for the operation of radio base stations (RBS) in telecommunication companies. Global navigation satellite system (GNSS) is an existing technology to provide precise timing information to distributed RBSs. GNSS timing receiver is used for providing higher timing accuracy than normal GNSS receiver in this synchronization domain.In this thesis, an experiment method for GNSS timing receiver performance in urban canyon has been designed and implemented to evaluate information and the quality of the one pulse per second (1PPS) signal generated by two different GNSS timing receivers. Multi-path signals and the gathered satellite geometry caused by poor sky visibility is identified as the main influential factors to the performance of the GNSS timing receivers. A mathematical model has been built for estimating the multi-path effect. GNSS planning tools are used to simulate the number of line-of-sight (LOS) satellites and Dilution of Precision (DOP) value.Sentinel is a 1PPS signal analyzing equipment from Calnex. Sentinel has an embedded rubidium clock, GNSS antenna, and receiver, and it can produce 1PPS signals to be used as a reference. In this report, we installed our GNSS antenna of Sentinel on the roof and test GNSS antenna in two specified positions representing urban canyon and rooftop. Recorded NMEA messages from GNSS receiver can help us to study the number of visible satellites, PDOP value and multi-path signals in realistic situations.The results show how the noise and time phase of 1PPS signals will be influenced in urban canyons. Since, the geometry of used satellites is similar to the rooftop situation, the multi-path effect of signals is identified as the main reason of this difference.This information is useful when telecommunication companies want to install their radio base station in urban canyons. It will help Ericsson to understand how their GNSS timing receiver is working and how the urban canyon will influence its performance. / Tidssynkronisering är kritisk för driften av radiobasstationer (RBS) i telekommunikationsföretag. Global Navigation Satellite System (GNSS) är en befintlig teknik för att ge exakt tidsinformation till distribuerade basstationer. GNSS-baserade tidsmottagare används för att ge högre timing-noggrannhet än vanlig GNSS mottagare i denna synkroniseringsdomän. I denna avhandling har en experimentmetod för GNSS-timingmottagarnas prestanda i urban canyon utformats och implementerats för att utvärdera den genererade informationen och kvaliteten på en puls per sekund-signal (1PPS). Flervägssignaler och den samlade satellitgeometrin som orsakas av dålig himmelsynlighet identifieras som de mest inflytelserika faktorerna för GNSS-tidsmottagarnas prestanda. En matematisk modell har donstruerats för att estimera multi-path-effekten. GNSS-planeringsverktyg används för att simulera antalet LOS-satelliter och DOP-värde (Dilution of Precision). Sentinel är en 1PPS signalanalysutrustning från Calnex. Sentinel har en inbyggd rubidiumklocka, GNSS-antenn och mottagare, och den kan producera 1PPS-signaler som ska användas som referens. I den här rapporten installerade vi vår GNSS-antenn på Sentinel på taket och GNSS-testantennen i två angivna positioner som representerar urban canyon och tak. Inspelade NMEA-meddelanden från GNSS-mottagare kan hjälpa oss att studera antalet synliga satelliter, PDOP-värde och flervägssignaler i realistiska scenarier. Resultatet visar att ljud- och tidsfasen för 1PPS-signaler påverkas i urban canyons. Eftersom satellitgeometrin liknar den för antenner placerade på taket, så är identifieras flervägsutbredningen som huvudorsak för denna skillnad. Denna information är användbar när telekommunikationsföretag vill installera sina radiobasstationer i urban canyons. Det kommer att hjälpa Ericsson att förstå hur deras GNSS-timingmottagare arbetar och hur urban canyon påverkar dess prestanda.

All-optical synchronization and its application in advanced optical communications have been investigated in this dissertation. Dynamics of all-optical timing synchronization (clock recovery) using multi-section gain-coupled distributed-feedback (MS-GC DFB) lasers are discussed. A record speed of 180-GHz timing synchronization has been demonstrated using this device. An all-optical carrier synchronization (phase and polarization recovery) scheme from PSK (phase shift keying) data is proposed and demonstrated for the first time. As an application of all-optical synchronization, the characterization of advanced modulation formats using a linear optical sampling technique was studied. The full characterization of 10-Gb/s RZ-BPSK (return-to-zero binary PSK) data has been demonstrated. Fast lockup and walk-off of the all-optical timing synchronization process on the order of nanoseconds were measured in both simulation and experiment. Phase stability of the recovered clock from a pseudo-random bit sequence signal can be achieved by limiting the detuning between the frequency of free-running self-pulsation and the input bit rate. The simulation results show that all-optical clock recovery using TS-DFB lasers can maintain a better than 5 % clock phase stability for large variations in power, bit rate and optical carrier frequency of the input data and therefore is suitable for applications in ultrafast optical packet switching. All-optical timing synchronization of 180-Gb/s data streams has been demonstrated using a MS-GC DFB laser. The recovered clock has a jitter of less than 410 fs over a dynamic range of 7 dB. All-optical carrier synchronization from phase modulated data utilizes a phase sensitive oscillator (PSO), which used a phase sensitive amplifier (PSA) as a gain block. Furthermore, all-optical carrier synchronization from 10-Gb/s BPSK data was demonstrated in experiment. The PSA is configured as a nonlinear optical loop mirror (NOLM). A discrete linear system analysis was carried out to understand the stability of the PSO. Complex envelope measurement using coherent linear optical sampling with mode-locked sources is investigated. It is shown that reliable measurement of the phase requires that one of the optical modes of the sampling pulses be locked to the optical carrier of the data signal to be measured. Carrier-envelope offset (CEO) is found to have a negligible effect on the measurement. Measurement errors of the intensity profile and phase depend on the pulsewidth and chirp of the sampling pulses as well as the detuning between the carrier frequencies of the data signal and the center frequency of the sampling source. Characterization of the 10-Gb/s RZ-BPSK signal was demonstrated using the coherent detection technique. Measurements of the optical intensity profile, chirp and constellation diagram were demonstrated. A CW local oscillator was used and electrical sampling was performed using a sampling scope. A novel feedback scheme was used to stabilize homodyne detection.

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Estrus synchronization (ES) is a valuable technology that can help beef cow-calf producers to overcome infertility caused by prolonged anestrus. Protocols for ES that use progesterone (P4) supplementation are of particular value to cows with prolonged postpartum anestrus as P4 triggers them to begin cycling and allows them to have fertility similar to that of cycling cows. Supplementation of P4 intravaginally with the use of a controlled internal drug release device (CIDR) improves cycle induction when compared to oral administration of P4. Vaginitis has been reported as a side effect to CIDR use in cattle, which raises concerns about its downstream effects on fertility. More specifically, the effects of CIDR use on the vaginal environment requires exploration, as no studies have explored the changes in vaginal microbiome in response to CIDR based ES protocols. In cattle, the vaginal microbiome has not been widely explored. On the contrary, the human vaginal microbiome is a well-defined environment, rich in bacteria from the genus Lactobacillus, which are responsible for promoting an environment of acidic pH. The dominance of Lactobacillus in the human vagina, however, fluctuates according to steroid hormone concentrations, and disruptions in the vaginal environment will cause depletion of Lactobacillus species, increase in vaginal pH and decreased fertility. Based on this data in humans, our objectives were to describe incidence of vaginitis caused by the CIDR in beef cows, as well as the vaginal microbiome changes in response to CIDR based protocols, and explore their relation to fertility. We found high incidences of vaginitis caused by CIDR use, yet CIDR-induced vaginitis did not negatively affect pregnancy outcomes. However, at CIDR withdrawal, there was decreased bacterial diversity, increased vaginal pH, increased bacterial abundance, and increased vaginal inflammation when compared to what was observed prior to CIDR insertion. Furthermore, abundance of bacteria, vaginal inflammation, and bacterial diversity, but not vaginal pH, were restored to normal values by the day of timed artificial insemination. This important finding suggests that although the vaginal microbiome was disrupted by the use of CIDR, the vaginal microbiome is resilient and capable of restoring its natural conditions without intervention. Finally, cows that ultimately became pregnant were found to have had increased bacterial diversity and decreased vaginal pH prior to protocol initiation, suggesting that the vaginal microbiome may play a role in individual cow fertility. In conclusion, our results indicate that for beef cows a more diverse vaginal microbiome with decreased vaginal pH presents greater resilience of the microbiome towards disruptions caused by an ES protocol, which is translated in greater pregnancy success. / Doctor of Philosophy / According to the Food and Agriculture Organization, the world population is expected to grow by 51% by the year of 2100. The efficiency of food production must therefore be optimized, given the finite availability of farmable land. In beef production, cow fertility is of great importance, since it will ultimately determine the number of animals available for slaughter. The main reproductive issue that cow-calf producers face is that after calving, cows will undergo a period known as postpartum anestrus, in which cows fail to ovulate. Artificial insemination (AI) can help to optimize beef production efficiency, since it allows for the dispersal of semen from valuable bulls to facilitate the genetic enhancement of herds. The use of estrus synchronization (ES) protocols allows for induction and synchronization of ovulation, which allows AI to be performed at the same time for large groups of cows. Progesterone is often used in ES protocols and is the hormone responsible for inducing cyclicity in postpartum cows. Progesterone can be administered either orally or intravaginally via the use of a controlled internal drug release (CIDR). While the CIDR seems to be more effective at inducing cyclicity of cattle compared to oral progesterone administration, vaginal inflammation as response to the CIDR has been reported in cattle. Little is known about the downstream effects of this inflammation on the normal vaginal microbiota and fertility in cattle. In humans, the vaginal microbiome is predominated by a single genus of bacteria (Lactobacillus), that has an essential role in producing lactic acid, which results in the human vagina being remarkably acidic. In humans, depletion of this bacteria, a condition called bacterial vaginosis (BV), allows for other types of bacteria to grow, which results in an increased vaginal pH and decreased fertility. The bovine vaginal microbiome composition and pH in response to the hormones administered during ES protocols and its relation to fertility have not been widely explored. Our objectives were to document the incidence of vaginitis caused by the CIDR in beef cows and evaluate its effects on the vaginal microbiome changes and fertility. We found high incidences of vaginitis caused by the CIDR, yet no effects of CIDR-induced vaginitis were seen on pregnancy success to the protocol. However, decreased bacterial diversity, followed by increases in vaginal pH, abundance of bacteria and vaginal inflammation are all detected at CIDR withdrawal when compared to before CIDR insertion. Furthermore, abundance of bacteria, vaginal inflammation, and bacterial diversity, but not vaginal pH, were restored to normal values by the day of timed AI, indicating that although the vaginal microbiome was disrupted using CIDR, the vaginal microbiome can restore to natural conditions, and indicate resilience of the vaginal microbiome. Finally, cows that became pregnant to the protocol presented increased bacterial diversity and decreased vaginal pH prior to the protocol. In conclusion, our results indicate that for beef cows a more diverse vaginal microbiome with decreased vaginal pH presents greater resilience of the microbiome towards disruptions caused by an ES protocol, which is translated in greater pregnancy success.

Dynamic Cellular Cognitive System (DCCS) serves as a cognitive network for white space devices in TV white space. It is also designed to provide quality communications for first responders in area with damaged wireless communication infrastructure. In DCCS network, diverse types of communication devices interoperate, communicate, and cooperate with high spectrum efficiency in a Dynamic Spectrum Access (DSA) scenario. DCCS can expand to a broad geographical distribution via linking to existing infrastructure. DCCS can quickly form a network to accommodate a diverse set of devices in natural disaster areas. It can also recover the infrastructure in a blind spot, for example, a subway or mountain area. Its portability and low cost make it feasible for commercial applications. This dissertation starts with an overview of DCCS network. DCCS defines a cognitive radio network and a set of protocols that each cognitive radio node inside the network must adopt to function as a user within the group. Multiple secondary users cooperate based on a fair and efficient scheme without losing the flexibility and self adaptation features. The basic unit of DCCS is a cell. A set of protocols and algorithms are defined to meet the communication requirement for intra-cell communications. DCCS includes multiple layers and multiple protocols. This dissertation gives a comprehensive description and analysis of building a DCCS network. It covers the network architecture, physical and Medium Access Control (MAC) layers for data and command transmission, spectrum management in DSA scenario, signal classification and synchronization and describes a working prototype of DCCS. Two key technologies of intra-cell communication are spectrum management and Universal Classification and Synchronization (UCS). A channel allocation algorithm based on calculating the throughput of an available is designed and the performance is analyzed. UCS is conceived as a self-contained system which can detect, classify, and synchronize with a received signal and extract all parameters needed for physical layer demodulation. It enables the accommodation of non-cognitive devices and improves communication quality by allowing a cognitive receiver to track physical layer changes at the transmitter. Inter-cell communications are the backhaul connections of DCCS. This dissertation discusses two approaches to obtaining spectrum for inter-cell communications. A temporary leasing approach focuses on the policy aspects, and the other approach is based on using OFDMA to combine separate narrowband channels into a wideband channel that can meet the inter-cell communications throughput requirements. A prototype of DCCS implemented on GNU radio and USRP platform is included in the dissertation. It serves as the proof of concept of DCCS. / Ph. D.

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