437 research outputs found
A Beta-Beta Achievability Bound with Applications
A channel coding achievability bound expressed in terms of the ratio between
two Neyman-Pearson functions is proposed. This bound is the dual of a
converse bound established earlier by Polyanskiy and Verd\'{u} (2014). The new
bound turns out to simplify considerably the analysis in situations where the
channel output distribution is not a product distribution, for example due to a
cost constraint or a structural constraint (such as orthogonality or constant
composition) on the channel inputs. Connections to existing bounds in the
literature are discussed. The bound is then used to derive 1) an achievability
bound on the channel dispersion of additive non-Gaussian noise channels with
random Gaussian codebooks, 2) the channel dispersion of the exponential-noise
channel, 3) a second-order expansion for the minimum energy per bit of an AWGN
channel, and 4) a lower bound on the maximum coding rate of a multiple-input
multiple-output Rayleigh-fading channel with perfect channel state information
at the receiver, which is the tightest known achievability result.Comment: extended version of a paper submitted to ISIT 201
Beta-Beta Bounds: Finite-Blocklength Analog of the Golden Formula
It is well known that the mutual information between two random variables can
be expressed as the difference of two relative entropies that depend on an
auxiliary distribution, a relation sometimes referred to as the golden formula.
This paper is concerned with a finite-blocklength extension of this relation.
This extension consists of two elements: 1) a finite-blocklength channel-coding
converse bound by Polyanskiy and Verd\'{u} (2014), which involves the ratio of
two Neyman-Pearson functions (beta-beta converse bound); and 2) a novel
beta-beta channel-coding achievability bound, expressed again as the ratio of
two Neyman-Pearson functions.
To demonstrate the usefulness of this finite-blocklength extension of the
golden formula, the beta-beta achievability and converse bounds are used to
obtain a finite-blocklength extension of Verd\'{u}'s (2002) wideband-slope
approximation. The proof parallels the derivation of the latter, with the
beta-beta bounds used in place of the golden formula.
The beta-beta (achievability) bound is also shown to be useful in cases where
the capacity-achieving output distribution is not a product distribution due
to, e.g., a cost constraint or structural constraints on the codebook, such as
orthogonality or constant composition. As an example, the bound is used to
characterize the channel dispersion of the additive exponential-noise channel
and to obtain a finite-blocklength achievability bound (the tightest to date)
for multiple-input multiple-output Rayleigh-fading channels with perfect
channel state information at the receiver.Comment: to appear in IEEE Transactions on Information Theor
Analysis of Fisher Information and the Cram\'{e}r-Rao Bound for Nonlinear Parameter Estimation after Compressed Sensing
In this paper, we analyze the impact of compressed sensing with complex
random matrices on Fisher information and the Cram\'{e}r-Rao Bound (CRB) for
estimating unknown parameters in the mean value function of a complex
multivariate normal distribution. We consider the class of random compression
matrices whose distribution is right-orthogonally invariant. The compression
matrix whose elements are i.i.d. standard normal random variables is one such
matrix. We show that for all such compression matrices, the Fisher information
matrix has a complex matrix beta distribution. We also derive the distribution
of CRB. These distributions can be used to quantify the loss in CRB as a
function of the Fisher information of the non-compressed data. In our numerical
examples, we consider a direction of arrival estimation problem and discuss the
use of these distributions as guidelines for choosing compression ratios based
on the resulting loss in CRB.Comment: 12 pages, 3figure
Fundamental limits of many-user MAC with finite payloads and fading
Consider a (multiple-access) wireless communication system where users are
connected to a unique base station over a shared-spectrum radio links. Each
user has a fixed number of bits to send to the base station, and his signal
gets attenuated by a random channel gain (quasi-static fading). In this paper
we consider the many-user asymptotics of Chen-Chen-Guo'2017, where the number
of users grows linearly with the blocklength. In addition, we adopt a per-user
probability of error criterion of Polyanskiy'2017 (as opposed to classical
joint-error probability criterion). Under these two settings we derive bounds
on the optimal required energy-per-bit for reliable multi-access communication.
We confirm the curious behaviour (previously observed for non-fading MAC) of
the possibility of perfect multi-user interference cancellation for user
densities below a critical threshold. Further we demonstrate the suboptimality
of standard solutions such as orthogonalization (i.e., TDMA/FDMA) and treating
interference as noise (i.e. pseudo-random CDMA without multi-user detection).Comment: 38 pages, conference version accepted to IEEE ISIT 201
Minimum Energy to Send Bits Over Multiple-Antenna Fading Channels
This paper investigates the minimum energy required to transmit
information bits with a given reliability over a multiple-antenna Rayleigh
block-fading channel, with and without channel state information (CSI) at the
receiver. No feedback is assumed. It is well known that the ratio between the
minimum energy per bit and the noise level converges to dB as goes
to infinity, regardless of whether CSI is available at the receiver or not.
This paper shows that lack of CSI at the receiver causes a slowdown in the
speed of convergence to dB as compared to the case of
perfect receiver CSI. Specifically, we show that, in the no-CSI case, the gap
to dB is proportional to , whereas when perfect
CSI is available at the receiver, this gap is proportional to . In
both cases, the gap to dB is independent of the number of transmit
antennas and of the channel's coherence time. Numerically, we observe that,
when the receiver is equipped with a single antenna, to achieve an energy per
bit of dB in the no-CSI case, one needs to transmit at least information bits, whereas bits suffice for the case of
perfect CSI at the receiver
Interference Alignment with Limited Feedback on Two-cell Interfering Two-User MIMO-MAC
In this paper, we consider a two-cell interfering two-user multiple-input
multiple-output multiple access channel (MIMO-MAC) with limited feedback. We
first investigate the multiplexing gain of such channel when users have perfect
channel state information at transmitter (CSIT) by exploiting an interference
alignment scheme. In addition, we propose a feedback framework for the
interference alignment in the limited feedback system. On the basis of the
proposed feedback framework, we analyze the rate gap loss and it is shown that
in order to keep the same multiplexing gain with the case of perfect CSIT, the
number of feedback bits per receiver scales as , where and denote the number of
transmit antennas and a constant, respectively. Throughout the simulation
results, it is shown that the sum-rate performance coincides with the derived
results.Comment: 6 pages, 2 figures, Submitted ICC 201
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
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