Krishnan Eswaran

Secrecy via sources and channels — A secret key - Secret message rate tradeoff region

Alice and Bob want to share a secret key and to communicate an independent message, both of which they desire to be kept secret from an eavesdropper Eve. We study this problem of secret communication and secret key generation when two resources are available - correlated sources at Alice, Bob, and Eve, and a noisy broadcast channel from Alice to Bob and Eve. No other resource, in particular, no other channel is available. We are interested in characterizing the fundamental trade-off between the rates of the secret message and secret key. We present an achievable solution based on a separation architecture and prove its optimality under three settings: when Eves source and channel are degraded versions of Bobs, and either Bobs source or channel is by itself useless in generating a secret key.

Zero-Rate Feedback Can Achieve the Empirical Capacity

The utility of limited feedback for coding over an individual sequence of discrete memoryless channels is investigated. This study complements recent results showing how limited or noisy feedback can boost the reliability of communication. A strategy with fixed input distribution P is given that asymptotically achieves rates arbitrarily close to the mutual information induced by P and the state-averaged channel. When the capacity-achieving input distribution is the same over all channel states, this achieves rates at least as large as the capacity of the state-averaged channel, sometimes called the empirical capacity.

Secrecy via Sources and Channels

Alice and Bob want to share a secret key and to communicate an independent message, both of which they desire to be kept secret from an eavesdropper Eve. This problem of secret communication and secret-key generation when two resources are available-correlated sources at Alice, Bob, and Eve, and a noisy broadcast channel from Alice to Bob and Eve which is independent of the sources is studied. The goal is to characterize the fundamental tradeoff between the rates of the secret message and secret key. An achievable solution and proof of its optimality for the parallel channels and sources case when each subchannel and source component satisfies a degradation order (either in favor of the legitimate receiver or the eavesdropper) is presented. This includes the case of jointly Gaussian sources and an additive Gaussian channel, for which the secrecy region is evaluated.

Cognitive Radio Through Primary Control Feedback

A fundamental problem in dynamic frequency reuse is that the cognitive radio is ignorant of the amount of interference it inflicts on the primary license holder. Policies that attempt to limit interference without the active participation of the primary are thus difficult to implement. However, many wireless systems use flow control feedback such as ARQs. By listening to these control signals, a cognitive radio can obtain indirect information about the interference it generates and thus behave in an acceptable manner. This paper introduces an information-theoretic model of this basic observation and develops and analyzes algorithms that can exploit it. In particular, a simple generic strategy is proposed where the cognitive radio monitors the primarys effective packet rate and only transmits when that rate is above a threshold. The strategy is shown to have important universality properties with respect to unknown time-varying interference characteristics as well as favorable delay properties.

Achievable rates for conferencing multiway channels

A generalization of the additive Gaussian two-way channel to M users is considered. Such channels contain implicit feedback in the sense that the channel output signals observed by the different encoders are correlated. While the benefits of feedback are shown to be negligible at high SNR, for moderate SNR, feedback can play a significant role in boosting the sum-rate performance. To highlight this potential gain, the special case of the M-user multiway channel with a common output is considered. By taking insights from Kramerpsilas Fourier MEC, a feedback strategy is introduced and shown to strictly dominate the performance of a pre-log optimal non-feedback strategy. Furthermore, an upper bound is derived to show this feedback strategy achieves the sum-rate capacity beyond a certain SNR threshold. Under per-symbol power constraints, this upper bound can be tightened to show the feedback strategy is sum-rate optimal for all SNR values.

On the quadratic AWGN CEO problem and non-gaussian sources

In the CEO problem, introduced by Berger et al, IEEE Trans. Info. Theory, 1996, a CEO is interested in a source that cannot be observed directly. M agents observe independently noisy versions of the source and, without collaborating, must encode these across noiseless rate-constrained channels to the CEO. The quadratic AWGN CEO problem refers to the class of CEO problems for which the agents view the source through additive white Gaussian noise, and the distortion is squared error. This paper discusses two upper bounds to the CEO sum-rate distortion function for this class of problems. The first follows from elementary arguments. It permits two conclusions. First, the worst case is when the underlying source is Gaussian (for fixed variance). Second, there are source distributions that lead to a significantly better behavior. The second upper bound follows from a new bound on the rate loss between the CEO and the remote rate-distortion function. For certain source distributions and certain ranges of distortion, this bound is better than the first

Using zero-rate feedback on binary additive channels with individual noise sequences

Recently, Shayevitz and Feeler introduced an individual sequence formulation of channel coding under model uncertainty and an elegant coding strategy that adapts Horsteins scheme to this setting to achieve the empirical capacity of the channel. Their scheme requires both full-rate output feedback and common randomness. We present a strategy in the style of Hybrid ARQ that requires no output feedback by using common randomness and zero-rate active feedback. This strategy still asymptotically achieves the empirical capacity.

Achievable Error Exponents in Multiterminal Source Coding

Encoding correlated sources at separate encoders has been studied extensively from the perspective of asymptotically long block codes. The associated error exponents are known for the case of lossless source coding. In this paper, we introduce a novel technique for deriving achievable error exponents for lossy source coding problems, where the original sources need to be reconstructed to within some fidelity. As an example, we show how to apply our technique to determine achievable error exponents for the Berger-Yeung problem.

Secret communication using sources and channels

Alice wants to send Bob a secret message in the presence of an eavesdropper Eve. Alice has two resources available: a noisy broadcast channel and source observations correlated with observations at Bob and Eve. We consider two cases, the first in which the source observations and channel are independent and the second in which they can depend on each other. For the independent case, we consider a strategy that exploits the sources and channels separately and show this separation strategy is optimal for a class of sources and channels that includes a Gaussian example. For the case in which the sources and channels depend on each other, this separation strategy does not work, and an optimal strategy has yet to be established. For this setting, we improve on the best known upper bound to the secret message capacity.

An observation about feedback from cognitive radio

While it is well known that feedback does not increase the capacity of discrete memoryless channels, this note examines a discrete memoryless channel with a cost constraint at the output. When that cost constraint has memory, i.e., depends on several past channel outputs, it is demonstrated that the gap between the feedback and non-feedback capacities can be unbounded. One motivation for such channel output constraints with memory comes from cognitive radio applications in which the constraints depend on how the cognitive radio activity interferes with the primary user.