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# Title:Zero-Error Capacity of $P$-ary Shift Channels and FIFO Queues

Abstract: 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.
 Comments: 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) Subjects: Information Theory (cs.IT); Discrete Mathematics (cs.DM) MSC classes: 94A24, 94A40, 94B25, 94B50 Journal reference: IEEE Trans. Inform. Theory, vol. 63, no. 12, pp. 7698--7707, Dec. 2017 DOI: 10.1109/TIT.2017.2756667 Cite as: arXiv:1605.02441 [cs.IT] (or arXiv:1605.02441v2 [cs.IT] for this version)
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