Channel codes enable reliable transmission of information. For this reason, they are widely used in applications like mobile communication networks, server farms, fiber-optic communication, DVD, Blue Rays, deep space communication and many more. Now, how easy is it to find a “good” channel code? It was known that, under some conditions, if you pick at random from all possible codes you are likely to get a good one. So, we wondered: ok, but how good? In our new paper, presented at the IEEE International Symposium on Information Theory 2021, we make a step towards the answer to this question. We quantify how good a typical code is, providing a lower bound on “how fast” its error probability vanishes.
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Thiswork was funded by: Beatriu de Pinós fellowship programme / Secretary of Universities and Research (Government of Catalonia), European Union’s Horizon 2020 research and innovation programme / Marie Skłodowska-Curie grant agreement No. 801370, European Research Council under ERC grant agreement 725411.