The development of information society is closely connected and depends on the development of data storage, data securing and data search tools. These tools can be improved in two ways, which can be notionally named ‘physical’ and ‘programming’. The second one is less consuming, since it makes possible to store more data on the same drive, to search data faster or to transmit them more securely by the same communication channel only due to applying more sophisticated mathematical methods. These methods include, in the first place, the methods of data compression, noise resistance and data search. The research in question is intended to investigate and advance such methods.
C. Shannon, the founder of information theory, has established the theoretical thresholds for the efficiency of data compression and error correcting codes for specified data sources in the late 1940-th. Codes that allow us to compress the data very close to the theoretical threshold, are known since 1950-th, however, they are not so efficient by other measures, such as decoding speed, possibility to search compressed files directly and robustness in the sense of limiting the error propagation. And vice versa, the codes that benefit from the these properties, such as Fibonacci or byte-aligned codes, suffer from the low compression rate. Thus, the development of codes that combine a high compression rate with other useful properties is an actual task. This was one of the main goals of this thesis and it leaded us to multi-delimiter codes, which were defined in this thesis for the first time ever.
Also, the generalized mathematical apparatus for investigating the codes having aforementioned properties has not been developed by now. In this thesis, a splittability of codes is defined — the property, which makes the development of such mathematical apparatus possible. Basing on the splittability property, the completeness and universality of multi-delimiter coded has been proved, their asymptotic behavior has been established as well as some properties of error correcting schemas. Also, the advantages of multi-delimiter codes over Fibonacci codes, which are closest to them, were explained from the perspective of code’s structural specificity, namely by proving the fact that these two types of codes represent two different classes of splittable codes.
In the area of error-correcting coding, the best known by now codes, such as turbo codes, reduce the error rate significantly in the channels with relatively high or average signal-to-noise ratio. However, their efficiency falls down when this ratio reaches 1–2 dB or less. Such noise level can be considered as realistic when it comes, for instance, to transmitting a signal from remotely piloted aircrafts while radio interference is intentionally emitted. Therefore, the development of error correcting methods that minimalize the interference impact in a noised environment is an actual problem. And this problem was resolved to a great extent in the present research.
