## Tuesday, September 8, 2015

### My Story with Polar Codes

It was the end of August 2010, and the weather was unusually good in Dublin. During the breaks at the IEEE Information Theory Workshop we could easily go outside, sit in the grass, and discuss the previous talks. Well, some people discussed, some just listened. Since this was my first conference in information theory (I did not even have a paper there, my boss allowed me to go there without actively participating -- an opportunity I am extremely grateful for), I clearly belonged to the second group. But then, already on the second day, there were some talks I felt comfortable with: Erdal Arikan gave a lecture on Polar Codes, a new coding technique he invented recently. What followed were several talks related to polar coding, including talks from Emmanuel Abbe (who was my main source of inspiration for my investigation of the fractality of polar codes), Tanaka (who looked at the polar coding procedure from a stochastic dynamical system point-of-view), Ido Tal and Alexander Vardy (whose code construction technique was extremely useful in proving fractality), and Eran Hof. While I did not understand a lot from his talk, I owe Eran big time: Being a total noob, I did not know anybody at this conference, and he was so kind to introduce the "big players" to me. That was absolutely necessary, because during one of the breaks I approached Sergio Verdu and asked him about the polar code construction technique he just presented. Well, apparently I confused him with Alexander Vardy (I have no idea why). Anyways, although this was one of the best conferences I've ever been to (an excursion to Castle Malahide, Whiskey tasting at Jameson's, a Riverdance show during the conference dinner, a pleasant stay at a cute little hotel, great weather, nice people, and all this together with my back-then-future-wife), this was just the beginning of my interest in polar coding.

It was in November 2011 when I presented my first paper at an information theory-related conference, the ISWCS in Aachen (during one of the short coffee breaks I met Gerhard Kramer, my current boss, for the first time; I also met Georg Böcherer, just finishing his PhD and winning the best paper award). As usual for these conferences, the first day featured tutorials in the afternoon. One of these tutorials was on polar codes, held by Emmanuel Abbe. I still have the printed handouts; one of the few paper documents I moved from Graz to Munich. It was an unforgettable experience, partly because of the awesome presentation and Emmanuel's great didactic skills, partly because of Emmanuel's lively discussion with the audience (particularly with Tor Aulin). And this great impressions led me to think about possible research directions on the train ride home to Graz. In a document called "Resarch Ideas.txt" I wrote
If a channel (one of the partitioned channels) is already very good (close to perfect), is it possible to assume all its descendant channels to be good? [...] Can we use this to find an approximation of a "good" polar code?
And then nothing happened for quite some time, as I continued my PhD research on information loss in deterministic systems. All this time, these polar codes stayed in the back of my mind and came to the front whenever I attended a conference (there were ALWAYS talks on polar codes). But time went by fast, I finished my PhD and -- totally unexpected -- started working at the Institute for Communications Engineering in Munich, becoming a member of Gerhard's lab and Georg's colleague. Some months there, not much research done (I was busy writing project proposals), the whole lab took a skiing trip to the alps in South Tirol, disguised under the title "Joint Conference on Communications and Coding". Well, in fact we did more research than skiing, something which I am quite grateful for (there are some very embarrassing photos of me trying cross-country skiing...). Instead of presenting work already done, I presented open problems, among them some ideas about polar codes. The preparation for the talk inspired me to write a blog article, and soon after that all the questions in this article were answered. Emmanuel suggested via email to extend the analysis to Reed-Muller codes, which was completed almost equally fast. It was one of the very few lucky streaks I had in my research career so far, and still some open questions pester me.

Although I am not sure if any of the obtained results is useful, I'm extremely happy to have these things out of my mind (and in a paper on arXiv). I could also present these results at the NEWCOM# Emerging Topics Workshop in Cambridge. One of the participants of this workshop was Erdal Arikan, the father of polar codes, and the very same person we were sitting next to during the whiskey tasting event at Jameson's in Dublin five years ago.