A Note on Parallel Asynchronous Channels with Arbitrary Skews

A zero-error coding scheme of asymptotic rate $\log_2 (1+\sqrt{5}) - 1$ was recently described for a communication channel composed of parallel asynchronous lines satisfying the so-called no switch assumption. We prove that this is in fact the highest rate attainable, i.e., the zero-error capacity of this channel

Zero-Error Capacity of PP-ary Shift Channels and FIFO Queues

The objects of study of this paper are communication channels in which the dominant type of noise are symbol shifts, the main motivating examples being timing and bit-shift channels. Two channel models are introduced and their zero-error capacities and zero-error-detection capacities determined by explicit constructions of optimal codes. Model A can be informally described as follows: 1) The information is stored in an $n$-cell register, where each cell is either empty or contains a particle of one of $P$ possible types, and 2) due to the imperfections of the device each of the particles may be shifted several cells away from its original position over time. Model B is an abstraction of a single-server queue: 1) The transmitter sends packets from a $P$-ary alphabet through a queuing system with an infinite buffer and a First-In-First-Out (FIFO) service procedure, and 2) each packet is being processed by the server for a random number of time slots. More general models including additional types of noise that the particles/packets can experience are also studied, as are the continuous-time versions of these problems.Comment: 10 pages (double-column), 3 figures. v2: title changed, material reorganized. Accepted for publication in IEEE Transactions on Information Theory (the Appendix will not appear in the published article

Runlength-Limited Sequences and Shift-Correcting Codes: Asymptotic Analysis

This work is motivated by the problem of error correction in bit-shift channels with the so-called $(d,k)$ input constraints (where successive $1$'s are required to be separated by at least $d$ and at most $k$ zeros, $0 \leq d < k \leq \infty$). Bounds on the size of optimal $(d,k)$-constrained codes correcting a fixed number of bit-shifts are derived, with a focus on their asymptotic behavior in the large block-length limit. The upper bound is obtained by a packing argument, while the lower bound follows from a construction based on a family of integer lattices. Several properties of $(d, k)$-constrained sequences that may be of independent interest are established as well; in particular, the exponential growth-rate of the number of $(d, k)$-constrained constant-weight sequences is characterized. The results are relevant for magnetic and optical information storage systems, reader-to-tag RFID channels, and other communication models where bit-shift errors are dominant and where $(d, k)$-constrained sequences are used for modulation.Comment: 10 pages (double-column), 2 figures. To appear in IEEE Transactions on Information Theor