Polar Codes for error correction: Analysis and Decoding Algorithms

I Polar Codes sono la prima classe di codici a correzione d’errore di cui è stato dimostrato il raggiungimento della capacità per ogni canale simmetrico, discreto e senza memoria, grazie ad un nuovo metodo introdotto recentemente, chiamato ”Channel Polarization”. In questa tesi verranno descritti in dettaglio i principali algoritmi di codifica e decodifica. In particolare verranno confrontate le prestazioni dei simulatori sviluppati per il ”Successive Cancellation Decoder” e per il ”Successive Cancellation List Decoder” rispetto ai risultati riportati in letteratura. Al fine di migliorare la distanza minima e di conseguenza le prestazioni, utilizzeremo uno schema concatenato con il polar code come codice interno ed un CRC come codice esterno. Proporremo inoltre una nuova tecnica per analizzare la channel polarization nel caso di trasmissione su canale AWGN che risulta il modello statistico più appropriato per le comunicazioni satellitari e nelle applicazioni deep space. In aggiunta, investigheremo l’importanza di una accurata approssimazione delle funzioni di polarizzazione.

Quantum error correction with the IBM quantum experience

Mentre si svolgono operazioni su dei qubit, possono avvenire vari errori, modificando così l’informazione da essi contenuta. La Quantum Error Correction costruisce algoritmi che permettono di tollerare questi errori e proteggere l’informazione che si sta elaborando. Questa tesi si focalizza sui codici a 3 qubit, che possono correggere un errore di tipo bit-flip o un errore di tipo phase-flip. Più precisamente, all’interno di questi algoritmi, l’attenzione è posta sulla procedura di encoding, che punta a proteggere meglio dagli errori l’informazione contenuta da un qubit, e la syndrome measurement, che specifica su quale qubit è avvenuto un errore senza alterare lo stato del sistema. Inoltre, sfruttando la procedura della syndrome measurement, è stata stimata la probabilità di errore di tipo bit-flip e phase-flip su un qubit attraverso l’utilizzo della IBM quantum experience.

Performance Analysis of Topological Quantum Error Correcting Codes

In the last few years there has been a great development of techniques like quantum computers and quantum communication systems, due to their huge potentialities and the growing number of applications. However, physical qubits experience a lot of nonidealities, like measurement errors and decoherence, that generate failures in the quantum computation. This work shows how it is possible to exploit concepts from classical information in order to realize quantum error-correcting codes, adding some redundancy qubits. In particular, the threshold theorem states that it is possible to lower the percentage of failures in the decoding at will, if the physical error rate is below a given accuracy threshold. The focus will be on codes belonging to the family of the topological codes, like toric, planar and XZZX surface codes. Firstly, they will be compared from a theoretical point of view, in order to show their advantages and disadvantages. The algorithms behind the minimum perfect matching decoder, the most popular for such codes, will be presented. The last section will be dedicated to the analysis of the performances of these topological codes with different error channel models, showing interesting results. In particular, while the error correction capability of surface codes decreases in presence of biased errors, XZZX codes own some intrinsic symmetries that allow them to improve their performances if one kind of error occurs more frequently than the others.

Erasure error correcting codes applied to DTN communications.

The space environment has always been one of the most challenging for communications, both at physical and network layer. Concerning the latter, the most common challenges are the lack of continuous network connectivity, very long delays and relatively frequent losses. Because of these problems, the normal TCP/IP suite protocols are hardly applicable. Moreover, in space scenarios reliability is fundamental. In fact, it is usually not tolerable to lose important information or to receive it with a very large delay because of a challenging transmission channel. In terrestrial protocols, such as TCP, reliability is obtained by means of an ARQ (Automatic Retransmission reQuest) method, which, however, has not good performance when there are long delays on the transmission channel. At physical layer, Forward Error Correction Codes (FECs), based on the insertion of redundant information, are an alternative way to assure reliability. On binary channels, when single bits are flipped because of channel noise, redundancy bits can be exploited to recover the original information. In the presence of binary erasure channels, where bits are not flipped but lost, redundancy can still be used to recover the original information. FECs codes, designed for this purpose, are usually called Erasure Codes (ECs). It is worth noting that ECs, primarily studied for binary channels, can also be used at upper layers, i.e. applied on packets instead of bits, offering a very interesting alternative to the usual ARQ methods, especially in the presence of long delays. A protocol created to add reliability to DTN networks is the Licklider Transmission Protocol (LTP), created to obtain better performance on long delay links. The aim of this thesis is the application of ECs to LTP.

Dynamic characterisation of four nine-story large-panel R.C. buildings in Bishkek (Kyrgyzstan): A comparison between experimental ambient vibration analysis and numerical finite element modeling

With the outlook of improving seismic vulnerability assessment for the city of Bishkek (Kyrgyzstan), the global dynamic behaviour of four nine-storey r.c. large-panel buildings in elastic regime is studied. The four buildings were built during the Soviet era within a serial production system. Since they all belong to the same series, they have very similar geometries both in plan and in height. Firstly, ambient vibration measurements are performed in the four buildings. The data analysis composed of discrete Fourier transform, modal analysis (frequency domain decomposition) and deconvolution interferometry, yields the modal characteristics and an estimate of the linear impulse response function for the structures of the four buildings. Then, finite element models are set up for all four buildings and the results of the numerical modal analysis are compared with the experimental ones. The numerical models are finally calibrated considering the first three global modes and their results match the experimental ones with an error of less then 20%.

Modeling, characterization and microalgal cultivation in an airlift panel photobioreactors.

Microalgae cultures are attracting great attentions in many industrial applications. However, one of the technical challenges is to cut down the capital and operational costs of microalgae production systems, with special difficulty in reactor design and scale-up. The thesis work open with an overview on the microalgae cultures as a possible answer to solve some of the upcoming planet issues and their applications in several fields. After the work offers a general outline on the state of the art of microalgae culture systems, taking a special look to the enclosed photobioreactors (PBRs). The overall objective of this study is to advance the knowledge of PBRs design and lead to innovative large scale processes of microalgae cultivation. An airlift flat panel photobioreactor was designed, modeled and experimentally characterized. The gas holdup, liquid flow velocity and oxygen mass transfer of the reactor were experimentally determined and mathematically modeled, and the performance of the reactor was tested by cultivation of microalgae. The model predicted data correlated well with experimental data, and the high concentration of suspension cell culture could be achieved with controlled conditions. The reactor was inoculated with the algal strain Scenedesmus obliquus sp. first and with Chlorella sp. later and sparged with air. The reactor was operated in batch mode and daily monitored for pH, temperature, and biomass concentration and activity. The productivity of the novel device was determined, suggesting the proposed design can be effectively and economically used in carbon dioxide mitigation technologies and in the production of algal biomass for biofuel and other bioproducts. Those research results favored the possibility of scaling the reactor up into industrial scales based on the models employed, and the potential advantages and disadvantages were discussed for this novel industrial design.

Modelling and Verification of a Correction Factor to Evaluate the Efficiency of Solar Thermal Collectors with the Rapid Test Method

A new method for the evaluation of the efficiency of parabolic trough collectors, called Rapid Test Method, is investigated at the Solar Institut Jülich. The basic concept is to carry out measurements under stagnation conditions. This allows a fast and inexpensive process due to the fact that no working fluid is required. With this approach, the temperature reached by the inner wall of the receiver is assumed to be the stagnation temperature and hence the average temperature inside the collector. This leads to a systematic error which can be rectified through the introduction of a correction factor. A model of the collector is simulated with COMSOL Multipyisics to study the size of the correction factor depending on collector geometry and working conditions. The resulting values are compared with experimental data obtained at a test rig at the Solar Institut Jülich. These results do not match with the simulated ones. Consequentially, it was not pos-sible to verify the model. The reliability of both the model with COMSOL Multiphysics and of the measurements are analysed. The influence of the correction factor on the rapid test method is also studied, as well as the possibility of neglecting it by measuring the receiver’s inner wall temperature where it receives the least amount of solar rays. The last two chapters analyse the specific heat capacity as a function of pressure and tem-perature and present some considerations about the uncertainties on the efficiency curve obtained with the Rapid Test Method.