Zero-Error Capacity of a Class of Timing Channels

We analyze the problem of zero-error communication through timing channels that can be interpreted as discrete-time queues with bounded waiting times. The channel model includes the following assumptions: 1) Time is slotted, 2) at most $N$ "particles" are sent in each time slot, 3) every particle is delayed in the channel for a number of slots chosen randomly from the set $\{0, 1, \ldots, K\}$, and 4) the particles are identical. It is shown that the zero-error capacity of this channel is $\log r$, where $r$ is the unique positive real root of the polynomial $x^{K+1} - x^{K} - N$. Capacity-achieving codes are explicitly constructed, and a linear-time decoding algorithm for these codes devised. In the particular case $N = 1$, $K = 1$, the capacity is equal to $\log \phi$, where $\phi = (1 + \sqrt{5}) / 2$ is the golden ratio, and the constructed codes give another interpretation of the Fibonacci sequence.Comment: 5 pages (double-column), 3 figures. v3: Section IV.1 from v2 is replaced with Remark 1, and Section IV.2 is removed. Accepted for publication in IEEE Transactions on Information Theor

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

The Single Server Queue and the Storage Model: Large Deviations and Fixed Points

We consider the coupling of a single server queue and a storage model defined as a Queue/Store model in Draief et al. 2004. We establish that if the input variables, arrivals at the queue and store, satisfy large deviations principles and are linked through an {\em exponential tilting} then the output variables (departures from each system) satisfy large deviations principles with the same rate function. This generalizes to the context of large deviations the extension of Burke's Theorem derived in Draief et al. 2004.Comment: 20 page

The Binary Energy Harvesting Channel with a Unit-Sized Battery

We consider a binary energy harvesting communication channel with a finite-sized battery at the transmitter. In this model, the channel input is constrained by the available energy at each channel use, which is driven by an external energy harvesting process, the size of the battery, and the previous channel inputs. We consider an abstraction where energy is harvested in binary units and stored in a battery with the capacity of a single unit, and the channel inputs are binary. Viewing the available energy in the battery as a state, this is a state-dependent channel with input-dependent states, memory in the states, and causal state information available at the transmitter only. We find an equivalent representation for this channel based on the timings of the symbols, and determine the capacity of the resulting equivalent timing channel via an auxiliary random variable. We give achievable rates based on certain selections of this auxiliary random variable which resemble lattice coding for the timing channel. We develop upper bounds for the capacity by using a genie-aided method, and also by quantifying the leakage of the state information to the receiver. We show that the proposed achievable rates are asymptotically capacity achieving for small energy harvesting rates. We extend the results to the case of ternary channel inputs. Our achievable rates give the capacity of the binary channel within 0.03 bits/channel use, the ternary channel within 0.05 bits/channel use, and outperform basic Shannon strategies that only consider instantaneous battery states, for all parameter values.Comment: Submitted to IEEE Transactions on Information Theory, August 201

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

The single server queue and the storage model: Large deviations and fixed points

We consider the coupling of a single server queue and a storage model defined as a queue/store model. We establish that if the input variables, arrivals at the queue and store, satisfy large deviations principles and are linked through an exponential tilting, then the output variables (departures from each system) satisfy large deviations principles with the same rate function.Peer Reviewe

Information-theoretic analysis of human-machine mixed systems

Many recent information technologies such as crowdsourcing and social decision-making systems are designed based on (near-)optimal information processing techniques for machines. However, in such applications, some parts of systems that process information are humans and so systems are affected by bounded rationality of human behavior and overall performance is suboptimal. In this dissertation, we consider systems that include humans and study their information-theoretic limits. We investigate four problems in this direction and show fundamental limits in terms of capacity, Bayes risk, and rate-distortion. A system with queue-length-dependent service quality, motivated by crowdsourcing platforms, is investigated. Since human service quality changes depending on workload, a job designer must take the level of work into account. We model the workload using queueing theory and characterize Shannon's information capacity for single-user and multiuser systems. We also investigate social learning as sequential binary hypothesis testing. We find somewhat counterintuitively that unlike basic binary hypothesis testing, the decision threshold determined by the true prior probability is no longer optimal and biased perception of the true prior could outperform the unbiased perception system. The fact that the optimal belief curve resembles the Prelec weighting function from cumulative prospect theory gives insight, in the era of artificial intelligence (AI), into how to design machine AI that supports a human decision. The traditional CEO problem well models a collaborative decision-making problem. We extend the CEO problem to two continuous alphabet settings with general rth power of difference and logarithmic distortions, and study matching asymptotics of distortion as the number of agents and sum rate grow without bound