In this work, we investigate the design of the parity-check matrix in the recently introduced Syndrome-Based Neural Decoders, which are powerful neural-network-based channel decoders. We show that the structure of the parity-check matrix has a crucial effect on the decoder’s performance, propose an information-theoretic metric to describe this effect, and suggest an algorithm to construct a parity-check matrix accordingly. The results are illustrated both analytically and numerically, showing a considerable performance gain for the proposed design without any increase in training or decoding complexity.

In this work, we investigate the problem of neural-based error correction decoding, and more specifically, the new so-called syndrome-based decoding technique introduced to tackle scalability in the training phase for larger code sizes. We improve on previous works in terms of allowing full decoding of the message rather than codewords, allowing thus the application to non-systematic codes, and proving that the single-message training property is still viable. The suggested system is implemented and tested on polar codes of sizes (64,32) and (128,64), and a BCH of size (63,51), leading to a significant improvement in both Bit Error Rate (BER) and Frame Error Rate (FER), with gains between 0.3dB and 1dB for the implemented codes in the high Signal-to-Noise Ratio (SNR) regime.

In the present work, we investigate the construction and performances of practical wiretap polar codes which aim at transmitting a message reliably to a legitimate receiver (Bob) while keeping it concealed from an eavesdropper (Eve). We show that, unlike in the asymptotic scenario for which the proof of optimality of wiretap polar codes was derived, the construction of such codes for moderate blocklengths calls for a careful choice of some key design parameters, along with more rigorous formulae for the polarization steps.

Information leakage estimation for practical wiretap codes is a challenging task for which existing solutions are either too complex or suboptimal, and don't scale for large blocklengths. In this paper we present a new method, based on a modified version of the successive cancellation decoder in order to compute the information leakage for the wiretap polar code which improves upon existing methods in terms of complexity and accuracy. Results are presented for classical binary-input symmetric channels alike the Binary Erasure Channel (BEC), the Binary Symmetric Channel (BSC) and Binary Input Additive White Gaussian Noise channel (BI-AWGN).

This work investigates the general two-user compound Broadcast Channel (BC) in which an encoder wishes to transmit two private messages W1 and W2 to two receivers while being oblivious to the actual channel realizations controlling the communication. The focus is on the characterization of the largest achievable rate region by resorting to more involved encoding and decoding techniques than the usual coding schemes of the standard BC. Involved decoding schemes are first explored, and an achievable rate region is derived based on the principle of Interference Decoding (ID), in which each receiver decodes its intended message and chooses to (non-uniquely) decode, or not, the interfering non-itended message. This decoding scheme is shown to be capacity achieving for a class of non-trivial compound BEC/BSC broadcast channels while the worst-case of Marton's inner bound-based on No Interference Decoding (NID)-fails to achieve the capacity region. Involved encoding schemes are later investigated, and an achievable rate region is derived based on Multiple Description (MD) coding wherin the encoder transmits a common description as well as multiple dedicated private descriptions to the many possible channel realizations of the users. It turns out that MD coding yields larger inner bounds than the single description scheme-Common Description (CD) coding-for a class of compound Multiple Input Single Output Broadcast Channels (MISO BC).

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. In this model an encoder observes a pair of memoryless sources (Sn1, Sn2) and communicates with two receivers over a common error-free rate-limited link of capacity R0, as well as two individual error-free rate-limited links of capacities R1and R2. Both receivers reproduce the source component Sn2losslessly; and Receiver 1 also reproduces the source component Sn1lossily, to within some prescribed distortion level D1. Also, Receiver 1 and Receiver 2 observe each a memoryless side information sequence, Yn1and Yn2, assumed to be arbitrarily correlated among them, and with the source pair (Sn1, Sn2).

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.

The capacity region of the multicast Cognitive InterFerence Channel (CIFC) is investigated. This channel consists of two independent transmitters that wish to multicast two different messages, each to a different set of users. In addition, one of the transmitters-commonly referred to as the cognitive transmitter-has prior non-causal knowledge of both messages to be transmitted. This scenario subsumes some long-standing open problems, such as the interference channel, the broadcast channel, and multicast communications. The aim of this paper is the derivation of optimal interference mitigation techniques under different interference regimes. To this end, two settings, namely the multi-primary CIFC, i.e., M = 1 and N ≥ 1, and its complementary, the multi-secondary CIFC, i.e., N = 1 and M ≥ 1, are investigated as an attempt to build a thorough understanding for the more general multicast CIFC setting. It is shown that, for some interference regimes, well-known coding techniques for the standard CIFC remain still optimal under the constraint of multicasting to multiple users. However, in other interference regimes, capacity achieving coding and decoding schemes prove to be more involved. A careful combination of these coding schemes and new outer bounding techniques allows to characterize the capacity region for several classes of discrete memoryless and Gaussian multicast CIFC under different interference regimes.

In this work, we investigate two secure source coding models, a Helper problem and a Gray-Wyner problem. In both settings, the encoder is connected to each of the legitimate receivers through a public link as well as a private link; and an external eavesdropper intercepts every information that is sent on the public link. Specifically, in the Helper problem, a memoryless source pair (S0; S1) is to be compressed and sent on both links such that the component S0can be recovered losslessly at the legitimate receiver while being kept completely secret from an eavesdropper that overhears on the public link, and the component S1is recovered lossily, to within some prescribed distortion level, at the legitimate receiver. In the Gray-Wyner model, a memoryless source triple (S0; S1; S2) is to be compressed and sent to two legitimate receivers, such that the component S0is recovered at both receivers losslessly and kept secret at an external eavesdropper that listens on the public link; and the component Sj, is to be recovered lossily at Receiver j, j = 1, 2. We establish single-letter characterizations of the optimal secure rate-distortion regions of both models. The analysis sheds important light on the role of the private link(s), i.e., for the transmission of the source S0or for sharing a secret key that is then used to encrypt the source S0over the public link.

We investigate two classes of lossy source coding problems under equivocation constraints, namely, an instance of the Helper problem and a Gray-Wyner network model. In the instance of the Helper problem that we consider, an encoder communicates with a legitimate receiver over two links, a private link and a public link; and an external eavesdropper overhears the transmission on the public link. The encoder observes two arbitrarily correlated discrete memoryless sources (Sn0n, S1n) and wishes to transmit the component S1nto the legitimate receiver lossily while maintaining the equivocation about the two sources at the external eavesdropper no smaller than some prescribed level. We establish a single-letter characterization of the optimal rate-distortion-equivocation region of this model. The analysis sheds important light on the role of the private link in this setting. In the Gray-Wyner network model with secrecy constraints that we consider, two sources (Sn1n, S2n) need to be transmitted lossily each to one user while concealing them from an external eavesdropper that overhears the transmission on the common link. For this model as well, we establish a single-letter characterization of the optimal rate-distortion-equivocation region. In particular, we show how the imposed security constraint modifies the standard Gray-Wyner compression scheme.

In this paper, 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 the decoders, and the other is reproduced 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. In particular, we show that the optimal coding scheme for this setting is one in which the common description to be recovered by both the decoders should allow to involve all or part of the source that is to be reproduced at only one decoder. 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 the decoders) can share an exact copy of the compressed version of this source component, i.e., a common encoder-decoder reconstruction constraint. For this model as well, we establish a single-letter characterization of the associated rate-distortion function.

This work investigates the Multicast Cognitive Interference Channel (CIFC) where many secondary users are interested in the same cognitive message. The focus is to study the role that Multiple Description (MD) coding can play under simultaneous transmissions. Though for the very weak, very strong, and mixed very weak/strong interference regimes, resorting to a Common Description (CD) alone is capacity achieving, in the weak interference regime it becomes crucial to resort to a more evolved coding scheme relying on multiple descriptions that could each accommodate differently the interference experienced at the secondary users. A Gaussian example illustrates this claim and various capacity results are likewise reported.

The capacity of the Multicast Cognitive Interference Channel (CIFC), where many primary users are interested in the same message, is investigated. In the light of the existing results on the CIFC, capacity is characterized for the very weak and very strong interference regimes as well as the mixed weak/strong interference scenario through novel inner and outer bounds. Moreover, the capacity regions of the corresponding Gaussian settings are likewise reported.

This paper 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 nontrivial 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 semideterministic 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 and binary symmetric components.

This work investigates the secrecy capacity region of the Wiretap Broadcast Channel (WBC) where an encoder communicates two private messages over a Broadcast Channel (BC) while keeping both messages secret from the eavesdropper. Our main result is the derivation of a novel outer bound and an inner bound on the secrecy capacity region of this setting. These results allow us to characterize the capacity region for three non-degraded classes of WBCs: the deterministic and the semi-deterministic WBC with a more noisy eavesdropper, and the WBC when users exhibit less noisiness order between them.

This work investigates the “2 by 1” two-user Compound Broadcast Channel. We investigate an evolved encoding scheme, based on the use of Multiple Description (MD) coding, where the source transmits both common and private descriptions to the many channel instances of the same user. We derive the resulting MD inner bound and evaluate it for the compound MISO BC resorting to a Dirty Paper Code (DPC). The suggested MD-DPC “strictly” outperforms Common Description (CD)-DPC and hence, palliates better the effect of channel uncertainty.

This work investigates the general three-message compound broadcast channel (BC) where an encoder wishes to communicate a common and two private messages to two groups of users. We focus on the study of the largest achievable region when the encoder is constrained to use a single description per message that we refer to as “simplified random codes”. In this setting, we investigate the different roles that decoders can play at the destinations. Surprisingly enough, we show that simultaneous decoding of both the intended as well as the interference message at the destinations can strictly enlarge-in opposition with the standard BC- the rate region with respect to the worst-case (over all channels) of Marton's inner bound.