Anelia Somekh-Baruch

Capacity of Cognitive Interference Channels With and Without Secrecy

Like the conventional two-user interference channel, the cognitive interference channel consists of two transmitters whose signals interfere at two receivers. It is assumed that there is a common message (message 1) known to both transmitters, and an additional independent message (message 2) known only to the cognitive transmitter (transmitter 2). The cognitive receiver (receiver 2) needs to decode messages 1 and 2, while the non cognitive receiver (receiver 1) should decode only message 1. Furthermore, message 2 is assumed to be a confidential message which needs to be kept as secret as possible from receiver 1, which is viewed as an eavesdropper with regard to message 2. The level of secrecy is measured by the equivocation rate. In this paper, a single-letter expression for the capacity-equivocation region of the discrete memoryless cognitive interference channel is obtained. The capacity-equivocation region for the Gaussian cognitive interference channel is also obtained explicitly. Moreover, particularizing the capacity-equivocation region to the case without a secrecy constraint, the capacity region for the two-user cognitive interference channel is obtained, by providing a converse theorem.

On the capacity game of public watermarking systems

Watermarking codes are analyzed as a game between two players: an information hider and a decoder, on the one hand, and an attacker on the other hand. It is assumed that the covertext (the original data within which the message is hidden) is drawn from a memoryless stationary source and its realization is available at the information hider only. The information hider is allowed to cause some tolerable level of distortion to the covertext, and the resulting distorted data can suffer some additional amount of distortion caused by an attacker who aims at erasing the message. Motivated by a worst case approach, we assume that the attacker is informed of the hiding strategy taken by the information hider and the decoder, while they are uninformed of the attacking scheme. The capacity is expressed as the limit of a sequence of single-letter expressions under the assumption that the encoder uses constant composition codes.

On the error exponent and capacity games of private watermarking systems

Watermarking systems are analyzed as a game between an information hider, a decoder, and an attacker. The information hider is allowed to cause some tolerable level of distortion to the original data within which the message is hidden, and the resulting distorted data can suffer some additional amount of distortion caused by an attacker who aims at erasing the message. Two games are investigated: the error exponent game and the coding capacity game. Motivated by a worst case approach, we assume that the attacker is informed of the hiding strategy taken by the information hider and the decoder, which are uninformed of the attacking scheme. This approach leads to the maximin error exponent and maximin coding capacity as objective functions. It is assumed that the host data is drawn from a finite-alphabet memoryless stationary source, and its realization (side information) is available at the encoder and the decoder. A single-letter expression for the maximin error exponent is found under large deviations distortion constraints. Moreover, we find an asymptotically optimal random coding distribution, a universal decoder, and a worst case attack channel. It is proved that there is a saddle point in the asymptotic exponent and that the minimax and the maximin error exponents are equal. Finally, a single letter expression for the coding capacity, i.e., the maximin reliable information rate, is found.

On the capacity game of private fingerprinting systems under collusion attacks

The problem of fingerprinting in the presence of collusive attacks is considered. It is modeled as a game between a fingerprinter and a decoder on the one hand, and a coalition of two or more attackers on the other. The fingerprinter distributes, to different users, different fingerprinted copies of a host data (covertext ) embedded with different fingerprints. The coalition members create a forgery of the data while aiming at erasing the fingerprints in order not to be detected. Their action is modeled by a multiple-access channel (MAC). The decoder, who has access to the original covertext data, observes the forgery and decodes one of the messages in order to identify one of the members of the coalition. Motivated by a worst case approach, we assume that the coalition of attackers is informed of the hiding strategy taken by the fingerprinter and the decoder, while they are uninformed of the attacking scheme. A single-letter expression for the capacity is derived under the assumption that the host data is drawn from a memoryless stationary source and some mild assumptions on the operation of the encoder. It is shown that for a coalition consisting of L</spl infin/ members, the capacity scales with O(1/L), and whenever L grows with the length of the covertext, the capacity is essentially zero. Also, a lower bound on the error exponent is derived as a by-product of the achievability part, and asymptotically optimum strategies of the parties involved are characterized.

Message and State Cooperation in Multiple Access Channels

We investigate the capacity of a multiple access channel with cooperating encoders where partial state information is known to each encoder and full state information is known to the decoder. The cooperation between the encoders has a two-fold purpose: to generate empirical state coordination between the encoders, and to share information about the private messages that each encoder has. For two-way cooperation, this two-fold purpose is achieved by double-binning, where the first layer of binning is used to generate the state coordination similarly to the two-way source coding, and the second layer of binning is used to transmit information about the private messages. The complete result provides the framework and perspective for addressing a complex level of cooperation that mixes states and messages in an optimal way.

Cognitive interference channels with state information

Cognitive state-dependent interference channels are analyzed. We focus on the two-user case with two message sources. One of the transmitters, referred to as the cognitive informed user, knows both messages and also the states of the channel in a non-causal manner. The other transmitter knows only one of the messages and does not know the channel states. Each of the two decoders is supposed to decode only its intended message. Inner and outer bounds on the capacity region of this channel are provided for the general finite input alphabet case. The asymmetric state-dependent Gaussian weak interference channel with non-causal state information is then considered, and a closed form formula for the capacity region is established in the regime of weak interference.

Achievable Error Exponents for the Private Fingerprinting Game

Fingerprinting systems in the presence of collusive attacks are analyzed as a game between a fingerprinter and a decoder on the one hand, and a coalition of two or more attackers on the other hand. The fingerprinter distributes, to different users, different fingerprinted copies of a host data (covertext), drawn from a memoryless stationary source, embedded with different fingerprints. The coalition members create a forgery of the data while aiming at erasing the fingerprints in order not to be detected. Their action is modeled by a multiple-access channel (MAC). We analyze the performance of two classes of decoders, associated with different kinds of error events. The decoder of the first class aims at detecting the entire coalition, whereas the second is satisfied with the detection of at least one member of the coalition. Both decoders have access to the original covertext data and observe the forgery in order to identify member(s) of the coalition. Motivated by a worst case approach, we assume that the coalition of attackers is informed of the hiding strategy taken by the fingerprinter and the decoder, while they are uninformed of the attacking scheme. Achievable single-letter expressions for the two kinds of error exponents are obtained. Single-letter lower bounds are also derived for the subclass of constant composition codes. These lower and the upper bounds coincide for the error exponent of the first class. Further, for the error of the first kind, a decoder that is optimal is introduced, and the worst case attack channel is characterized

Twofold universal prediction schemes for achieving the finite-state predictability of a noisy individual binary sequence

The problem of predicting the next outcome of an individual binary sequence corrupted by noise using finite memory, is considered. The conditional finite-state (FS) predictability of an infinite individual sequence given its noisy version is defined as the minimum fraction of errors that can be made by any FS predictor fed by the noisy version. It is proved that the conditional FS predictability can be attained almost surely by universal sequential prediction schemes in the case where the noisy version is the output of a binary-symmetric channel (BSC) whose input is the clean individual sequence. In particular, universal predictors of the original noise-free setting, which operate on the noisy sequence, have this property. Moreover, these universal predictors do not depend on the crossover probability characterizing the BSC. It is seen that the noisy setting gives rise to additional criteria by which the performance of prediction schemes can be assessed. Finally, a closer look is taken at the conditional FS predictability, and this quantity is proposed as an additional measure of the complexity of a sequence, perhaps finer and more informative than the predictive complexity of the noise-free setting.

Exact Random Coding Exponents for Erasure Decoding

Random coding of channel decoding with an erasure option is studied. By analyzing the large deviations behavior of the code ensemble, we obtain exact single-letter formulas for the error exponents in lieu of Forneys lower bounds. The analysis technique we use is based on an enhancement and specialization of tools for assessing the statistical properties of certain distance enumerators. We specialize our results to the setup of the binary symmetric channel case with uniform random coding distribution and derive an explicit expression for the error exponent which, unlike Forneys bounds, does not involve optimization over two parameters. We also establish the fact that for this setup, the difference between the exact error exponent corresponding to the probability of undetected decoding error and the exponent corresponding to the erasure event is equal to the threshold parameter. Numerical calculations indicate that for this setup, as well as for a Z-channel, Forneys bound coincides with the exact random coding exponent.

On Gaussian wiretap channels with M-PAM inputs

This paper investigates the secrecy capacity of the Gaussian wiretap channel with M-PAM inputs, by capitalizing on the relationship between mutual information and minimum mean squared error (MMSE). In particular, we establish optimality conditions for both the M-PAM input power and the M-PAM input distribution, which we specialize to the asymptotic low-power and high-power regimes. By using the properties of the MMSE to establish sufficient conditions for the uniqueness of the solution of some of the underlying non-convex optimization problems, we also propose efficient algorithms to compute the optimal solutions. Interestingly, we show that with M-PAM inputs it is sub-optimal to use all the available power for some range of parameters — this is in sharp contrast to standard Gaussian channels. We also extend the results to the parallel Gaussian wiretap channel with M-PAM inputs. We put forth a mercury-waterfilling interpretation of the optimal power allocation procedure for parallel Gaussian wiretap channels which generalizes the conventional mercury-waterfilling interpretation for parallel Gaussian channels, with the mercury level amending the base level to account for both the non-Gaussianess of the input and the secrecy constraint.