I have long been wondering whether polar codes are fractal, found out that they are in 2015, and put a paper on arXiv. The story that began in 2010 finally comes to end -- the paper is now published!
I submitted the paper to the IEEE Transactions on Information Theory, where it was under review for 18 months. I was told that the two reviewers thought the paper collects a few "interesting and cute mathematical observations", but that it does not tell us anything about the relevant code properties such as error probabilities or code complexity. I was further told that if I could "add a convincing application", then the paper could get to a second review round.
I withdrew the paper and submitted it to Entropy, and open-access journal published by MDPI, in October 2017. I received reviews within less than two months. Four of the five reviewers were inclined to accept the paper after some revision, while the fifth reviewer insisted to reject the paper (and probably still does) because of its missing connection to real-world codes. It is worth mentioning that the review process was not only much faster than the one for the IEEE Transactions on Information Theory, but that I also got high-quality reviews: Some of the reviewers went through the math in detail, made corrections and suggestions for improvement that led to generalizing some of the results. This shows that a proper, high-quality review process cannot be used to justify long review cycles.