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

Some Aspects of Finite State Channel related to Hidden Markov Process

We have no satisfactory capacity formula for most channels with finite states. Here, we consider some interesting examples of finite state channels, such as Gilbert-Elliot channel, trapdoor channel, etc., to reveal special characters of problems and difficulties to determine the capacities. Meanwhile, we give a simple expression of the capacity formula for Gilbert-Elliot channel by using a hidden Markov source for the optimal input process. This idea should be extended to other finite state channels

Trade-off coding for universal qudit cloners motivated by the Unruh effect

A "triple trade-off" capacity region of a noisy quantum channel provides a more complete description of its capabilities than does a single capacity formula. However, few full descriptions of a channel's ability have been given due to the difficult nature of the calculation of such regions---it may demand an optimization of information-theoretic quantities over an infinite number of channel uses. This work analyzes the d-dimensional Unruh channel, a noisy quantum channel which emerges in relativistic quantum information theory. We show that this channel belongs to the class of quantum channels whose capacity region requires an optimization over a single channel use, and as such is tractable. We determine two triple-trade off regions, the quantum dynamic capacity region and the private dynamic capacity region, of the d-dimensional Unruh channel. Our results show that the set of achievable rate triples using this coding strategy is larger than the set achieved using a time-sharing strategy. Furthermore, we prove that the Unruh channel has a distinct structure made up of universal qudit cloning channels, thus providing a clear relationship between this relativistic channel and the process of stimulated emission present in quantum optical amplifiers.Comment: 26 pages, 4 figures; v2 has minor corrections to Definition 2. Definition 4 and Remark 5 have been adde