Error Free Perfect Secrecy Systems

Shannon's fundamental bound for perfect secrecy says that the entropy of the secret message cannot be larger than the entropy of the secret key initially shared by the sender and the legitimate receiver. Massey gave an information theoretic proof of this result, however this proof does not require independence of the key and ciphertext. By further assuming independence, we obtain a tighter lower bound, namely that the key entropy is not less than the logarithm of the message sample size in any cipher achieving perfect secrecy, even if the source distribution is fixed. The same bound also applies to the entropy of the ciphertext. The bounds still hold if the secret message has been compressed before encryption. This paper also illustrates that the lower bound only gives the minimum size of the pre-shared secret key. When a cipher system is used multiple times, this is no longer a reasonable measure for the portion of key consumed in each round. Instead, this paper proposes and justifies a new measure for key consumption rate. The existence of a fundamental tradeoff between the expected key consumption and the number of channel uses for conveying a ciphertext is shown. Optimal and nearly optimal secure codes are designed.Comment: Submitted to the IEEE Trans. Info. Theor

Capacity Analysis of Linear Operator Channels over Finite Fields

Motivated by communication through a network employing linear network coding, capacities of linear operator channels (LOCs) with arbitrarily distributed transfer matrices over finite fields are studied. Both the Shannon capacity $C$ and the subspace coding capacity $C_{\text{SS}}$ are analyzed. By establishing and comparing lower bounds on $C$ and upper bounds on $C_{\text{SS}}$, various necessary conditions and sufficient conditions such that $C=C_{\text{SS}}$ are obtained. A new class of LOCs such that $C=C_{\text{SS}}$ is identified, which includes LOCs with uniform-given-rank transfer matrices as special cases. It is also demonstrated that $C_{\text{SS}}$ is strictly less than $C$ for a broad class of LOCs. In general, an optimal subspace coding scheme is difficult to find because it requires to solve the maximization of a non-concave function. However, for a LOC with a unique subspace degradation, $C_{\text{SS}}$ can be obtained by solving a convex optimization problem over rank distribution. Classes of LOCs with a unique subspace degradation are characterized. Since LOCs with uniform-given-rank transfer matrices have unique subspace degradations, some existing results on LOCs with uniform-given-rank transfer matrices are explained from a more general way.Comment: To appear in IEEE Transactions on Information Theor

On Linear Operator Channels over Finite Fields

Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its input vector, and the transformation matrix is randomly and independently generated. The transformation matrix is assumed to remain constant for every T input vectors and to be unknown to both the transmitter and the receiver. There are NO constraints on the distribution of the transformation matrix and the field size. Specifically, the optimality of subspace coding over LOCs is investigated. A lower bound on the maximum achievable rate of subspace coding is obtained and it is shown to be tight for some cases. The maximum achievable rate of constant-dimensional subspace coding is characterized and the loss of rate incurred by using constant-dimensional subspace coding is insignificant. The maximum achievable rate of channel training is close to the lower bound on the maximum achievable rate of subspace coding. Two coding approaches based on channel training are proposed and their performances are evaluated. Our first approach makes use of rank-metric codes and its optimality depends on the existence of maximum rank distance codes. Our second approach applies linear coding and it can achieve the maximum achievable rate of channel training. Our code designs require only the knowledge of the expectation of the rank of the transformation matrix. The second scheme can also be realized ratelessly without a priori knowledge of the channel statistics.Comment: 53 pages, 3 figures, submitted to IEEE Transaction on Information Theor

Localization method for device-to-device through user movement

International audienceIndoor positioning system is a key component for developing various location based services such as indoor navigation in large complex buildings (e.g., commercial center and hospital). Meanwhile, it is challenging to design a cost effective solution which is able to provide high accuracy. A new method, namely Two-Step Movement (2SM), was proposed in [1] to demonstrate how to build a positioning system which requires only one Reference Point (RP) by exploiting user movement. The method can offer good precision and minimize the number of RPs required so as to reduce system implementation cost. Built on 2SM, here we first improve the positioning performance through multi-sampling technique to combat measurement noise. Secondly, we propose the Generalized Two-Step Movement (G2SM) method for device-to-device (D2D) systems in which both the mobile terminal (MT) and RP can be mobile device. The mobile user's position can be derived analytically and given in simple closed-form expression. Its effectiveness in the presence of noise is shown in simulation results

On the Peak-to-Average Power Ratio of Pre-Equalized Base-Field Hartley OFDM

International audienceWe show by the analytical and simulation results that pre-equalized OFDM based on base-field Hartley transform (BHT-OFDM), which is an alternative air interface for LTE-beyond or 5G, provides significantly better PAPR performance than conventional OFDM systems. We develop a tractable analytical closed-form expression of the statistical distribution of PAPR of pre-equalized BHT-OFDM based on correlated multivariate Rayleigh distributions and verify the result with comprehensive simulation studies. Comparisons show that the analytical and simulation results are consistent. Our study suggests that pre-equalized BHT-OFDM is not only favorable due to its inherent error correction capability but is also highly recommendable for its superiority in power efficiency beyond today's OFDM scheme

Alleviating poverty in Hong Kong : the evolution of policy decisions and instruments

published_or_final_versionPolitics and Public AdministrationMasterMaster of Public Administratio