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

TL;DR

This paper investigates the zero-error capacity of symbol-shift channels, modeling timing and FIFO queue systems, and provides explicit code constructions for optimal error detection and correction.

Contribution

Introduces two models of shift channels, derives their zero-error capacities, and constructs optimal codes for error detection and correction.

Findings

Explicit zero-error capacity formulas for both models

Optimal codes for error detection and correction

Extension to more general and continuous-time models

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.