  In this article, we investigate strategic information transmission over a
noisy channel. This problem has been widely investigated in Economics, when the
communication channel is perfect. Unlike in Information Theory, both encoder
and decoder have distinct objectives and choose their encoding and decoding
strategies accordingly. This approach radically differs from the conventional
Communication paradigm, which assumes transmitters are of two types: either
they have a common goal, or they act as opponent, e.g. jammer, eavesdropper. We
formulate a point-to-point source-channel coding problem with state
information, in which the encoder and the decoder choose their respective
encoding and decoding strategies in order to maximize their long-run utility
functions. This strategic coding problem is at the interplay between
Wyner-Ziv's scenario and the Bayesian persuasion game of Kamenica-Gentzkow. We
characterize a single-letter solution and we relate it to the previous results
by using the concavification method. This confirms the benefit of sending
encoded data bits even if the decoding process is not supervised, e.g. when the
decoder is an autonomous device. Our solution has two interesting features: it
might be optimal not to use all channel resources; the informational content
impacts the encoding process, since utility functions capture preferences on
source symbols.
