Covert Bits Through Queues

We consider covert communication using a queuing timing channel in the presence of a warden. The covert message is encoded using the inter-arrival times of the packets, and the legitimate receiver and the warden observe the inter-departure times of the packets from their respective queues. The transmitter and the legitimate receiver also share a secret key to facilitate covert communication. We propose achievable schemes that obtain non-zero covert rate for both exponential and general queues when a sufficiently high rate secret key is available. This is in contrast to other channel models such as the Gaussian channel or the discrete memoryless channel where only $\mathcal{O}(\sqrt{n})$ covert bits can be sent over $n$ channel uses, yielding a zero covert rate.Comment: To appear at IEEE CNS, October 201

Bits through queues with feedback

In their $1996$ paper Anantharam and Verd\'u showed that feedback does not increase the capacity of a queue when the service time is exponentially distributed. Whether this conclusion holds for general service times has remained an open question which this paper addresses. Two main results are established for both the discrete-time and the continuous-time models. First, a sufficient condition on the service distribution for feedback to increase capacity under FIFO service policy. Underlying this condition is a notion of weak feedback wherein instead of the queue departure times the transmitter is informed about the instants when packets start to be served. Second, a condition in terms of output entropy rate under which feedback does not increase capacity. This condition is general in that it depends on the output entropy rate of the queue but explicitly depends neither on the queue policy nor on the service time distribution. This condition is satisfied, for instance, by queues with LCFS service policies and bounded service times

On the reliability exponent of the exponential timing channel

Cataloged from PDF version of article.We determine the reliability exponent E(R) of the Anantharam-Verdu exponential server timing channel with service rate p for all rates R between a critical rate R-c = (mu/4) log 2 and the channel capacity C = e(-1)mu. For rates between 0 and R-c, we provide a random-coding lower bound E,(R) and a sphere-packing upper bound E-r(R) on E(R). We also determine that the cutoff rate R-0 for this channel equals mu/4, thus answering a question posed by Sundaresan and Verdu. An interesting aspect of our results is that the lower bound E, (R) for the reliability exponent of the timing channel coincides with Wyner's reliability exponent for the photon-counting channel with no dark current and with peak power constraint mu. Whether the reliability exponents of the two channels are actually equal everywhere remains open. This shows that the exponential server timing channel is at least as reliable as this type of a photon-counting channel for all rates

Feedback Increases the Capacity of Queues with Bounded Service Times

In the "Bits Through Queues" paper, it was conjectured that full feedback always increases the capacity of first-in-first-out queues, except when the service time distribution is memoryless. More recently, a non-explicit sufficient condition on the service time under which feedback increases capacity was provided, along with simple examples of service times satisfying this condition. In this paper, it is shown that full feedback increases the capacity of queues with bounded service times. This result is obtained by investigating a generalized notion of feedback, with full feedback and weak feedback as particular cases.Comment: 10 pages; two-colum

Capacity-Approaching Practical Codes for Queueing Channels: An Algebraic, State-Space, Message-Passing Approach

This report introduces a coding theory for queueing channels and discusses a practical capacity-approaching scheme. Here we consider a communication channel where the encoder communicates information based upon timings between successive packets. A receiver observes packet timings after they have traveled through a communication network with queues at intermediate router nodes. Based upon the encoding mechanism, the statistical structure of the network queues, and the packet timings it observes, the receiver finds the most likely bit sequence. Despite queueing system being nonlinear, non-stationary, and non-memoryless, Verdu and Anantharam provided a closed-form theoretical characterization of the maximum amount of information (i.e. capacity, in bits per second) that can be reliably communicated across a queue in their Information Theory Society Best Paper Award-Winning manuscript “Bits Through Queues”. However, to date, there has been a lack of practical ways to realize these theoretical possibilities. Indeed, the authors themselves claimed in 1998 that ‘Coding theory for queueing channels is virtually nonexistent.’ Here we introduce an architecture - based on algebraic codes, a state-space perspective on queues, and iterative message-passing on graphs – that is capacity-approaching and has low decoding complexity. To the best of the authors' knowledge, this is the first known such scheme.Ope