Zero-Error Shift-Correcting and Shift-Detecting Codes. Article Swipe
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· 2016
· Open Access
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· OA: W2381678937
Motivated by communication scenarios such as timing channels (in queuing systems, molecular communications, etc.) and bit-shift channels (in magnetic recording systems), we study the error control problem in cases where the dominant type of noise are symbol shifts. In particular, two channel models are introduced and their zero-error capacities determined by an explicit construction of optimal zero-error codes. Model A can be informally described as follows: 1) The information is stored in an n-cell register, where each cell can either be left empty, or can contain a particle of one of P possible types, and 2) due to the imperfections of the device every particle is shifted k cells away from its original position over time, where k is drawn from a certain range of integers, without the possibility of reordering particles. Model B is an abstraction of a singleserver queue: 1) The transmitter sends symbols/packets from a P -ary alphabet through a queuing system with an infinite buffer, and 2) each packet is being processed by the server for a number of time slots k ∈ {0, 1, . . . ,K}. Several variations of the above models are also discussed, e.g., with multiple particles per cell, with additional types of noise, and the continuous-time case. The models are somewhat atypical due to the fact that the length of the channel output in general differs from that of the corresponding input, and that this length depends on the noise (shift) pattern as well as on the input itself. This will require the notions of a zero-error code and the zero-error capacity, as introduced by Shannon, to be generalized.
