3 research outputs found
The Price of Uncertain Priors in Source Coding
We consider the problem of one-way communication when the recipient does not
know exactly the distribution that the messages are drawn from, but has a
"prior" distribution that is known to be close to the source distribution, a
problem first considered by Juba et al. We consider the question of how much
longer the messages need to be in order to cope with the uncertainty about the
receiver's prior and the source distribution, respectively, as compared to the
standard source coding problem. We consider two variants of this uncertain
priors problem: the original setting of Juba et al. in which the receiver is
required to correctly recover the message with probability 1, and a setting
introduced by Haramaty and Sudan, in which the receiver is permitted to fail
with some probability . In both settings, we obtain lower bounds that
are tight up to logarithmically smaller terms. In the latter setting, we
furthermore present a variant of the coding scheme of Juba et al. with an
overhead of bits, thus also establishing the
nearly tight upper bound.Comment: To appear in IEEE Transactions on Information Theor