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.

Abstract-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.

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.M. Benammar is with the Mathematics and Algorithmic Sciences Lab.,

Faster-than-Nyquist (FTN) transmission is a promising technique to increase spectral efficiency at fixed constellation size. However, traditional timing synchronization algorithms mostly rely on the eye diagram opening after matched-filtering (e.g., Gardner, zero-crossing). Such approaches are thus unsuitable in presence of FTN-induced intersymbol interference. In this paper, we first show that FTN signals exhibit cyclostationarity at the lth-order (l > 2) according to their bandwidth and symbol period. Then, we derive non-data-aided timing offset estimators from the cyclic temporal cumulant function. Besides its relevance for strong FTN scenarios, the proposed solution is also robust to frequency and phase offsets.

Abstract: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 (S n 1 , S n 2 ) and communicates with two receivers over an error-free rate-limited link of capacity R 0 , as well as error-free rate-limited individual links of capacities R 1 to the first receiver and R 2 to the second receiver. Both receivers reproduce the source component S n 2 losslessly; and Receiver 1 also reproduces the source component S n 1 lossily, to within some prescribed fidelity level D 1 . In addition, Receiver 1 and Receiver 2 are equipped, respectively, with memoryless side information sequences Y n 1 and Y n 2 . Important in this setup, the side information sequences are arbitrarily correlated among them, and with the source pair (S n 1 , S n 2 ); 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.