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.

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.