Core Concepts
The author explores the construction and properties of maximum length RLL sequences in de Bruijn graphs, focusing on reducing redundancy and improving efficiency.
Abstract
The content delves into the concept of RLL sequences within de Bruijn graphs for quantum communication synchronization. It proposes an algorithm to construct these sequences efficiently, discussing their applications and generalizations. The analysis includes detailed explanations, proofs, and computations related to the enumeration and characteristics of these sequences.
Stats
The number of (n, 1)-words is given by gn = 1.618^n - 0.618^n√5.
The number of (n, s)-words hn,s can be expressed as λ^(k+1)(λ - 1) / ((s + 2)λ - 2(s + 1) + 0.5), where λ satisfies xs+1 - Σxi = 0.
The length of a maximum length (n, s)-sequence is hn,s - Σi=1^s i * hn-2s-3+i,s.