As a CSoI Channels Scholar, I am expected to post every week about my undergraduate research project. Unfortunately, I do not yet know what exactly I am doing for my research project. Hopefully, this will be figured out soon.
Up to this point, I have been reading. I have read chapters 1 and 2 of Thomas Cover's Elements of Information Theory. I have also been attempting to read a paper written by my professor (which is a bit...dense). Currently, I am trying to read Shannon's original paper on "Communication Theory of Secrecy System". I doubt that reading this paper will have any direct effect on coming up with a project idea, however, I felt like I needed to read it anyways, since almost every academic paper I have read since the beginning of this summer cited this one paper. Luckily, I am finding Shannon's paper to be very interesting. The paper goes through the setup of the secrecy system, something I know about, but for the first time, I am reading about the motivations for why it is that way. I am also learning about ideas I have never considered before, like pure systems and residue classes. What surprised me the most about this paper, is that Shannon is a pretty good writer. Some people just have unlimited ability.
Last Tuesday, I attended a meeting that Professor Cuff holds for his grad students. At this meeting, he presented a few brain teaser questions, one of which I wanted to present to the curious folks reading this blog:
Suppose you have a sequence of N bits to communicate. What is the lowest number of bits you can send through a reliable channel, such that the receiver is guaranteed to correctly receive N-1 bits?
(Some clarification: Before you transmit your bits, you can choose to encode them in some way. The encoder will transform your N bits into say K bits. These K bits will be sent through the channel. The receiver knows your encoding scheme and can decode the K bits accordingly. The point of this problem is to find an encoding scheme which is lossy, so that the receiver might decode one bit incorrectly but he can accurately decode every other bit. You can choose which bit is lost for each string of bits. What is the smallest possible K?)
Aside from the brain teasers, I also saw a presentation by one of my professor's grad students. I will be meeting with this grad student tomorrow to come up with project ideas.
