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How much information can be carried over a wireless network with a multiplicity of nodes? What are the optimal strategies for information transmission and cooperation among the nodes? We obtain sharp information theoretic scaling laws under some conditions.

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Abstract — The minimum energy required to transmit a bit of information through a network characterizes the most economical way to communicate in a network. In this paper, we show that under a layered model of wireless networks, the minimum energyper-bit for multicasting in a mobile ad hoc network can be found by a linear program; the minimum energy-per-bit can be attained by performing network coding. Compared with conventional routing solutions, network coding not only promises a potentially lower energy-per-bit, but also enables the optimal solution to be found in polynomial time, in sharp contrast with the NPhardness of constructing the minimum-energy multicast tree as the optimal routing solution. We further show that the minimum energy multicast formulation is equivalent to a cost minimization with linear edge-based pricing, where the edge prices are the energy-per-bits of the corresponding physical broadcast links. This paper also investigates minimum energy multicasting with routing. Due to the linearity of the pricing scheme, the minimum energy-per-bit for routing is achievable by using a single distribution tree. A characterization of the admissible rate region for routing with a single tree is presented. The minimum energy-per-bit for multicasting with routing is found by an integer linear program. We show that the relaxation of this integer linear program, studied earlier in the Steiner tree literature, can now be interpreted as the optimization for minimum energy multicasting with network coding. In short, this paper presents a unifying study of minimum energy multicasting with network coding and routing. Index Terms — Network coding, routing, multicast, Steiner tree, wireless ad hoc networks, energy efficiency, mobility.

Abstract—We propose a scalar upper bound on the capacity region of the isotropic fading vector broadcast channel in terms of the capacity region of a scalar fading broadcast channel. The scalar upper bound is applicable to the broad class of isotropic fading broadcast channels regardless of the distribution of the users ’ channel magnitudes, the distribution of the additive noise experienced by each user, or the amount of channel knowledge available at the receiver. Using this upper bound, we prove the optimality of the Alamouti scheme in a broadcast setting, extend the recent results on the capacity of nondegraded, fading scalar broadcast channels to nondegraded fading vector broadcast channels, and determine the capacity region of a fading vector Gaussian broadcast channel with channel magnitude feedback. We also provide an example of a Rayleigh-fading broadcast channel with no channel state information available to the receiver (CSIR), where the bound on the capacity region obtained by a naive application of the scalar upper bound is provably loose, because it fails to account for the additional loss in degrees of freedom due to lack of channel knowledge at the receiver. A tighter upper bound is obtained by separately accounting for the loss in degrees of freedom due to lack of CSIR before applying the scalar upper bound. Index Terms—Broadcast channel, channel capacity, channel state information, degrees of freedom, fading channels, multiple antennas. I.

In this paper, we consider the Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap channel in which a transmitter wants to have confidential communication with an arbitrary number of users in the presence of an external eavesdropper. We derive the secrecy capacity region of this channel for the most general case. We first show that even for the single-input single-output (SISO) case, existing converse techniques for the Gaussian scalar broadcast channel cannot be extended to this secrecy context, to emphasize the need for a new proof technique. Our new proof technique makes use of the relationships between the minimum-mean-square-error and the mutual information, and equivalently, the relationships between the Fisher information and the differential entropy. Using the intuition gained from the converse proof of the SISO channel, we first prove the secrecy capacity region of the degraded MIMO channel, in which all receivers have the same number of antennas, and the noise covariance matrices can be arranged according to a positive semi-definite order. We then generalize this result to the aligned case, in which all receivers have the same number of antennas, however there is no order among the noise covariance matrices. We accomplish this task by using the channel enhancement technique. Finally, we find the secrecy capacity region of the general MIMO channel by using some limiting arguments on the secrecy capacity region of the aligned MIMO channel. We show that the capacity achieving coding scheme is a variant of dirty-paper coding with Gaussian signals.

Abstract — New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of n independent random variables to the information contained in sums over subsets of the random variables, for an arbitrary collection of subsets. As a consequence, a simple proof of the monotonicity of information in central limit theorems is obtained, both in the setting of i.i.d. summands as well as in the more general setting of independent summands with variancestandardized sums. Index Terms — Central limit theorem; entropy power; information inequalities. I.

We study di#erent notions of capacity for time-slotted ALOHA systems. In these systems multiple users synchronously send packets in a bursty manner over a common additive white Gaussian noise (AWGN) channel. The users do not coordinate their transmissions, which may collide at the receiver. For such a system we define both single-slot capacity and multiple-slot capacity. We then construct a coding and decoding scheme for single-slot capacity that achieves any rate within this capacity region. This coding and decoding scheme for a single time slot combines aspects of multiple access rate splitting and of broadcast codes for degraded AWGN channels. This design allows some bits to be reliably received even when collisions occur, and more bits to be reliably received in the absence of collisions. The exact number of bits reliably received under both of these scenarios is part of the code design process, which we optimize to maximize the expected rate in each slot.

Abstract—Security of quantization index modulation (QIM) watermarking methods is usually sought through a pseudorandom dither signal which randomizes the codebook. This dither plays the role of the secret key (i.e., a parameter only shared by the watermarking embedder and decoder), which prevents unauthorized embedding and/or decoding. However, if the same dither signal is reused, the observation of several watermarked signals can provide sufficient information for an attacker to estimate the dither signal. This paper focuses on the cases when the embedded messages are either known or constant. In the first part of this paper, a theoretical security analysis of QIM data hiding measures the information leakage about the secret dither as the mutual information between the dither and the watermarked signals. In the second part, we show how set-membership estimation techniques successfully provide accurate estimates of the dither from observed watermarked signals. The conclusion of this twofold study is that current QIM watermarking schemes have a relative low security level against this scenario because a small number of observed watermarked signals yields a sufficiently accurate estimate of the secret dither. The analysis presented in this paper also serves as the basis for more involved scenarios. Index Terms—Equivocation, lattice data hiding, mutual information, quantization index modulation, set-membership estimation, watermarking security. I.

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