Lossless Data Compression by Representing Data as a Solution to the Diophantine Equations

I am serving as a chair of Karandeep Singh Grewal’s Graduate Supervisory Committee. The committee includes, as members, Dr. Ajay Bansal and Dr. Michael Findler.

The thesis defense is scheduled for April 16, 2021, at 3:00 pm MST.


There has been a substantial development in the field of data transmission in the last two decades. One does not have to wait much for a high-definition video to load on the systems anymore. Data compression is one of the most prime technologies that helped achieve this seamless data transmission experience. It helps to store or send more data using lesser memory or network resources. However, it appears that there is a limit on the amount of compression that can be achieved with the existing lossless data compression techniques because they rely on the frequency of characters or set of characters in the data. This thesis proposes a lossless data compression technique in which the data is compressed by representing it as a set of parameters that can reproduce the original data without any loss when given to the corresponding mathematical equation. The mathematical equation used in the thesis is the sum of the first N terms in a geometric series. Various changes are made to this mathematical equation so that any given data can be compressed and decompressed. According to the proposed technique, the whole data is taken as a single decimal number and replaced with one of the terms of the used equation. All the other terms of the equation are computed and stored as a compressed file. The performance of the developed technique is evaluated in terms of compression ratio, compression time and decompression time. The evaluation metrics are then compared with the other existing techniques of the same domain.