Rate-Distortion Function for a Heegard-Berger Problem with Two Sources and Degraded Reconstruction sets

In this work, we investigate an instance of the Heegard-Berger problem with two sources and arbitrarily correlated side information sequences at two decoders, in which the reconstruction sets at the decoders are degraded. Specifically, two sources are to be encoded in a manner that one of the two is reproduced losslessly by both decoders, and the other is reproduced to within some prescribed distortion level at one of the two decoders. We establish a single-letter characterization of the rate-distortion function for this model. The investigation of this result in some special cases also sheds light on the utility of joint compression of the two sources. Furthermore, we also generalize our result to the setting in which the source component that is to be recovered by both users is reconstructed in a lossy fashion, under the requirement that all terminals (i.e., the encoder and both decoders) can share an exact copy of the compressed version of this source component, i.e., a common encoder-decoders reconstruction constraint. For this model as well, we establish a single-letter characterization of the associated rate-distortion function.Comment: Submitted to IEEE Trans. on Information Theor

Secrecy Capacity Region of Some Classes of Wiretap Broadcast Channels

This work investigates the secrecy capacity of the Wiretap Broadcast Channel (WBC) with an external eavesdropper where a source wishes to communicate two private messages over a Broadcast Channel (BC) while keeping them secret from the eavesdropper. We derive a non-trivial outer bound on the secrecy capacity region of this channel which, in absence of security constraints, reduces to the best known outer bound to the capacity of the standard BC. An inner bound is also derived which follows the behavior of both the best known inner bound for the BC and the Wiretap Channel. These bounds are shown to be tight for the deterministic BC with a general eavesdropper, the semi-deterministic BC with a more-noisy eavesdropper and the Wiretap BC where users exhibit a less-noisiness order between them. Finally, by rewriting our outer bound to encompass the characteristics of parallel channels, we also derive the secrecy capacity region of the product of two inversely less-noisy BCs with a more-noisy eavesdropper. We illustrate our results by studying the impact of security constraints on the capacity of the WBC with binary erasure (BEC) and binary symmetric (BSC) components.Comment: 19 pages, 8 figures, To appear in IEEE Trans. on Information Theor

Multi-Kernel Polar Codes: Proof of Polarization and Error Exponents

In this paper, we investigate a novel family of polar codes based on multi-kernel constructions, proving that this construction actually polarizes. To this end, we derive a new and more general proof of polarization, which gives sufficient conditions for kernels to polarize. Finally, we derive the convergence rate of the multi-kernel construction and relate it to the convergence rate of each of the constituent kernels.Comment: Accepted and to be presented at ITW 2017, Kaohsiun

Rate-Distortion Region of a Gray–Wyner Model with Side Information

In this work, we establish a full single-letter characterization of the rate-distortion region of an instance of the Gray–Wyner model with side information at the decoders. Specifically, in this model, an encoder observes a pair of memoryless, arbitrarily correlated, sources (Sn1,Sn2) and communicates with two receivers over an error-free rate-limited link of capacity R0 , as well as error-free rate-limited individual links of capacities R1 to the first receiver and R2 to the second receiver. Both receivers reproduce the source component Sn2 losslessly; and Receiver 1 also reproduces the source component Sn1 lossily, to within some prescribed fidelity level D1 . In addition, Receiver 1 and Receiver 2 are equipped, respectively, with memoryless side information sequences Yn1 and Yn2 . Important in this setup, the side information sequences are arbitrarily correlated among them, and with the source pair (Sn1,Sn2) ; and are not assumed to exhibit any particular ordering. Furthermore, by specializing the main result to two Heegard–Berger models with successive refinement and scalable coding, we shed light on the roles of the common and private descriptions that the encoder should produce and the role of each of the common and private links. We develop intuitions by analyzing the developed single-letter rate-distortion regions of these models, and discuss some insightful binary examples

On linear MMSE based turbo-equalization of nonlinear Volterra channels

International audienceThis article deals with Minimum Mean Square Error (MMSE) turbo equalization of nonlinear interference using a volterra series decomposition of the underlying nonlinear channel. Although it has been often argued that linear MMSE based equalization is unsuited for cancelling nonlinear interference, we show that this common belief is not true in a strict sense. By a proper derivation of the linear based MMSE soft equalizer, we are able to show that the underlying structure of the equalizer is equivalent to a Soft Interference Canceller (SIC) treating both the linear and nonlinear interference. Based on these results, approximations are provided for lowering the computational complexity. Links to previously proposed “nonlinear” SIC are emphasized showing that the previously proposed structures are nothing but approximations of a linear MMSE receiver applied to nonlinear ISI channels. Simulations show that significant improvements can be achieved by using the proposed exact and approximate MMSE based turbo-equalizers

Asymptotic Analysis and Design of Iterative Receivers for Non Linear ISI Channels

International audienceIn this paper, iterative receiver analysis and design for non linear satellite channels is investigated. To do so, an EXtrinsic Information Transfer (EXIT) chart-based optimization is applied using two major assumptions: the equalizer outputs follow a Gaussian Mixture distribution since we use non-binary modulations and partial interleavers are used between the Low Density Parity Check (LDPC) code and the mapper. Achievable rates, performance and thresholds of the optimized receiver are analysed. The objective in fine is to answer the question: Is it worth optimizing an iterative receiver for non linear satellite channels

Neural Networks-Based Turbo Equalization of a Satellite Communication Channel

International audienceThis paper proposes neural networks-based turbo equalization (TEQ) applied to a non linear channel. Based on a Volterra model of the satellite non linear communication channel, we derive a soft input soft output (SISO) radial basis function (RBF) equalizer that can be used in an iterative equalization in order to improve the system performance. In particular, it is shown that the RBF-based TEQ is able to achieve its matched filter bound (MFB) within few iterations. The paper also proposes a blind implementation of the TEQ using a multilayer perceptron (MLP) as an adaptive model of the nonlinear channel. Asymptotic analysis as well as reduced complexity implementations are also presented and discussed

Development of instrumentation incorporating solid state gas sensors for measurement of oxygen partial pressure.

Electronic instrumentation was developed for the measurement of the oxygen partial pressure, P1 ( in a sample gas using fully-sealed zirconia pump-gauge oxygen sensors operated in an AC mode. These sensors, operated typically at 700°C, consisted of two discs of zirconia with porous platinum electrodes on each face separated by a gold seal and enclosing a small internal volume. One disc was operated as a pump enabling oxygen to be electrochemically transferred into and out of the enclosed volume; the other disc operated as a gauge, the Nernst EMF across the electrodes providing a measure of the ratio of the internal to the external oxygen partial pressure. By careful design of the circuitry it was possible to measure the oxygen partial pressure, P, without the need for a separate reference gas supply. Subsequently, a novel "tracking" mode of operation was proposed and implemented in which leakage effects generally associated with sealed pump-gauge devices were minimised: the sensor was operated in a feedback control-loop in order to adjust automatically the mean internal reference oxygen partial pressure, P0, so as to maintain the ratio (Px/P0) close to unity. The signal-to-noise ratio was markedly improved by using gauge EMFs with high amplitudes which inevitably display a distorted sinusoid due to the logarithmic term in the Nernst equation. Surprisingly, mathematical analysis predicted that the linearity of the output of the instrument using phase-sensitive detection should not be affected by the deviation from a sinusoid and this was confirmed experimentally: signal processing was practically implemented using simple analogue electronics. As anticipated there was a strong influence of sensor temperature on the output of the instrument: consequently, methods for temperature compensation were proposed and shown to be feasible with minimum hardware. The theory of Operation of leaky pump-gauge was also developed which indicated that a physical leak in the sensor should cause a phase shift and amplitude change in the sensor output. Experimental results were, in general, in agreement with the theory demonstrating the influences of the geometry and dimensions of the leak and of the operating frequency. Importantly, the theory predicted that, when operated in the AC mode, devices with major leakage may still be used for oxygen partial pressure measurement: again this was confirmed by experiment and the additional benefit of a concomitant substantial simplification of the electronic circuitry also realised. Interestingly an unexpected but small influence of oxygen concentration on the phase shift was observed: this requires additional study

On Linear Frequency Domain Turbo-Equalization of Non Linear Volterra Channels

International audienceThis article deals with iterative Frequency Domain Equalization (FDE) for Single Carrier (SC) transmissions over Volterra non linear satellite channels. SC-FDE has gained much importance in recent research for its efficient implementation at the receiver and its interesting low Peak to Average Power Ratio (PAPR) at the transmitter. However, nearly saturated power amplifiers on board satellites generate linear and non linear Inter Symbol Interference (ISI) at the receiver. It is thus interesting to investigate the implementation of SC-FDE for non linear channels. To do so, a frequency domain equivalent satellite channel is derived based on the time domain Volterra series representation of the non linear channel. Then a Minimum Mean Square Error (MMSE)-based iterative frequency domain equalizer is designed. It is shown that the proposed equalizer consists of a Soft Interference Canceller (SIC) which subtracts both the linear and non-linear soft frequency symbols. The equalizer performance is then compared to the equivalent time domain implementation. Results show that a channel-memory independent efficient implementation is achieved at the price of a negligible spectral efficiency loss due to cyclic prefix insertion