214 research outputs found
Exact Asymptotics for the Random Coding Error Probability
Error probabilities of random codes for memoryless channels are considered in
this paper. In the area of communication systems, admissible error probability
is very small and it is sometimes more important to discuss the relative gap
between the achievable error probability and its bound than to discuss the
absolute gap. Scarlett et al. derived a good upper bound of a random coding
union bound based on the technique of saddlepoint approximation but it is not
proved that the relative gap of their bound converges to zero. This paper
derives a new bound on the achievable error probability in this viewpoint for a
class of memoryless channels. The derived bound is strictly smaller than that
by Scarlett et al. and its relative gap with the random coding error
probability (not a union bound) vanishes as the block length increases for a
fixed coding rate.Comment: Full version of the paper in ISIT2015 with some corrections and
refinement
Optimality of Thompson Sampling for Gaussian Bandits Depends on Priors
In stochastic bandit problems, a Bayesian policy called Thompson sampling
(TS) has recently attracted much attention for its excellent empirical
performance. However, the theoretical analysis of this policy is difficult and
its asymptotic optimality is only proved for one-parameter models. In this
paper we discuss the optimality of TS for the model of normal distributions
with unknown means and variances as one of the most fundamental example of
multiparameter models. First we prove that the expected regret of TS with the
uniform prior achieves the theoretical bound, which is the first result to show
that the asymptotic bound is achievable for the normal distribution model. Next
we prove that TS with Jeffreys prior and reference prior cannot achieve the
theoretical bound. Therefore the choice of priors is important for TS and
non-informative priors are sometimes risky in cases of multiparameter models
Variable-to-Fixed Length Homophonic Coding Suitable for Asymmetric Channel Coding
In communication through asymmetric channels the capacity-achieving input
distribution is not uniform in general. Homophonic coding is a framework to
invertibly convert a (usually uniform) message into a sequence with some target
distribution, and is a promising candidate to generate codewords with the
nonuniform target distribution for asymmetric channels. In particular, a
Variable-to-Fixed length (VF) homophonic code can be used as a suitable
component for channel codes to avoid decoding error propagation. However, the
existing VF homophonic code requires the knowledge of the maximum relative gap
of probabilities between two adjacent sequences beforehand, which is an
unrealistic assumption for long block codes. In this paper we propose a new VF
homophonic code without such a requirement by allowing one-symbol decoding
delay. We evaluate this code theoretically and experimentally to verify its
asymptotic optimality.Comment: Full version of the paper to appear in 2017 IEEE International
Symposium on Information Theory (ISIT2017
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