An Extended Fano's Inequality for the Finite Blocklength Coding

Fano's inequality reveals the relation between the conditional entropy and the probability of error . It has been the key tool in proving the converse of coding theorems in the past sixty years. In this paper, an extended Fano's inequality is proposed, which is tighter and more applicable for codings in the finite blocklength regime. Lower bounds on the mutual information and an upper bound on the codebook size are also given, which are shown to be tighter than the original Fano's inequality. Especially, the extended Fano's inequality is tight for some symmetric channels such as the $q$-ary symmetric channels (QSC).Comment: 5 pages, 4 figures, submitted to IEEE ISIT 201

A Queueing Characterization of Information Transmission over Block Fading Rayleigh Channels in the Low SNR

Unlike the AWGN (additive white gaussian noise) channel, fading channels suffer from random channel gains besides the additive Gaussian noise. As a result, the instantaneous channel capacity varies randomly along time, which makes it insufficient to characterize the transmission capability of a fading channel using data rate only. In this paper, the transmission capability of a buffer-aided block Rayleigh fading channel is examined by a constant rate input data stream, and reflected by several parameters such as the average queue length, stationary queue length distribution, packet delay and overflow probability. Both infinite-buffer model and finite-buffer model are considered. Taking advantage of the memoryless property of the service provided by the channel in each block in the the low SNR (signal-to-noise ratio) regime, the information transmission over the channel is formulated as a \textit{discrete time discrete state} $D/G/1$ queueing problem. The obtained results show that block fading channels are unable to support a data rate close to their ergodic capacity, no matter how long the buffer is, even seen from the application layer. For the finite-buffer model, the overflow probability is derived with explicit expression, and is shown to decrease exponentially when buffer size is increased, even when the buffer size is very small.Comment: 29 pages, 11 figures. More details on the proof of Theorem 1 and proposition 1 can be found in "Queueing analysis for block fading Rayleigh channels in the low SNR regime ", IEEE WCSP 2013.It has been published by IEEE Trans. on Veh. Technol. in Feb. 201

Sparsifying the Fisher Linear Discriminant by Rotation

Many high dimensional classification techniques have been proposed in the literature based on sparse linear discriminant analysis (LDA). To efficiently use them, sparsity of linear classifiers is a prerequisite. However, this might not be readily available in many applications, and rotations of data are required to create the needed sparsity. In this paper, we propose a family of rotations to create the required sparsity. The basic idea is to use the principal components of the sample covariance matrix of the pooled samples and its variants to rotate the data first and to then apply an existing high dimensional classifier. This rotate-and-solve procedure can be combined with any existing classifiers, and is robust against the sparsity level of the true model. We show that these rotations do create the sparsity needed for high dimensional classifications and provide theoretical understanding why such a rotation works empirically. The effectiveness of the proposed method is demonstrated by a number of simulated and real data examples, and the improvements of our method over some popular high dimensional classification rules are clearly shown.Comment: 30 pages and 9 figures. This paper has been accepted by Journal of the Royal Statistical Society: Series B (Statistical Methodology). The first two versions of this paper were uploaded to Bin Dong's web site under the title "A Rotate-and-Solve Procedure for Classification" in 2013 May and 2014 January. This version may be slightly different from the published versio

Uplink Age of Information of Unilaterally Powered Two-way Data Exchanging Systems

We consider a two-way data exchanging system where a master node transfers energy and data packets to a slave node alternatively. The slave node harvests the transferred energy and performs information transmission as long as it has sufficient energy for current block, i.e., according to the best-effort policy. We examine the freshness of the received packets at the master node in terms of age of information (AoI), which is defined as the time elapsed after the generation of the latest received packet. We derive average uplink AoI and uplink data rate as functions of downlink data rate in closed form. The obtained results illustrate the performance limit of the unilaterally powered two-way data exchanging system in terms of timeliness and efficiency. The results also specify the achievable tradeoff between the data rates of the two-way data exchanging system.Comment: INFOCOM 2018 AOI Wkshp, 6 page