Antipowers in Uniform Morphic Words and the Fibonacci Word

Fici, Restivo, Silva, and Zamboni define a $k$-antipower to be a word composed of $k$ pairwise distinct, concatenated words of equal length. Berger and Defant conjecture that for any sufficiently well-behaved aperiodic morphic word $w$, there exists a constant $c$ such that for any $k$ and any index $i$, a $k$-antipower with block length at most $ck$ starts at the $i$th position of $w$. They prove their conjecture in the case of binary words, and we extend their result to alphabets of arbitrary finite size and characterize those words for which the result does not hold. We also prove their conjecture in the specific case of the Fibonacci word.

Age of Information Based URLLC-enabled UAV Wireless Communications System

<div>This paper considers an unmanned aerial vehicles (UAV) communication network, where UAV operate as an aerial mobile relay between a source and a destination of the network. To capture the “timeliness” of the received information at the destination node, a new performance metric named age of information (AoI) is considered. In addition, a short packet communication scheme maintains low latency in the proposed UAV wireless communication system. The finite block-length theory investigates the performances of short packet communications scheme in the UAV-assisted wireless communications system. In this paper, the Average Age of Information (AAoI) is estimated by applying the Stochastic Hybrid Systems (SHS) model. The SHS model comprises discrete states represents events that reset the AoI process and continuously dynamics that represent linearly growing age processes. Finally, a closed-form expression for the AAoI of the proposed UAV wireless communication system is derived and it can be used to estimate the optimal altitude, block length and other parameters.</div>

Age of Information Based URLLC-enabled UAV Wireless Communications System

<div>This paper considers an unmanned aerial vehicles (UAV) communication network, where UAV operate as an aerial mobile relay between a source and a destination of the network. To capture the “timeliness” of the received information at the destination node, a new performance metric named age of information (AoI) is considered. In addition, a short packet communication scheme maintains low latency in the proposed UAV wireless communication system. The finite block-length theory investigates the performances of short packet communications scheme in the UAV-assisted wireless communications system. In this paper, the Average Age of Information (AAoI) is estimated by applying the Stochastic Hybrid Systems (SHS) model. The SHS model comprises discrete states represents events that reset the AoI process and continuously dynamics that represent linearly growing age processes. Finally, a closed-form expression for the AAoI of the proposed UAV wireless communication system is derived and it can be used to estimate the optimal altitude, block length and other parameters.</div>