PAC Learnability for Reliable Communication over Discrete Memoryless Channels
CoRR(2024)
摘要
In practical communication systems, knowledge of channel models is often
absent, and consequently, transceivers need be designed based on empirical
data. In this work, we study data-driven approaches to reliably choosing
decoding metrics and code rates that facilitate reliable communication over
unknown discrete memoryless channels (DMCs). Our analysis is inspired by the
PAC learning theory and does not rely on any assumptions on the statistical
characteristics of DMCs. We show that a naive plug-in algorithm for choosing
decoding metrics is likely to fail for finite training sets. We propose an
alternative algorithm called the virtual sample algorithm and establish a
non-asymptotic lower bound on its performance. The virtual sample algorithm is
then used as a building block for constructing a learning algorithm that
chooses a decoding metric and a code rate using which a transmitter and a
receiver can reliably communicate at a rate arbitrarily close to the channel
mutual information. Therefore, we conclude that DMCs are PAC learnable.
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