核心概念
The authors provide explicit numerical procedures to solve optimization problems related to the Gilbert-Varshamov bound for constrained systems, improving upon previous works.
摘要
The content discusses evaluating the Gilbert-Varshamov bound for constrained systems, focusing on optimization problems and numerical procedures. It explores improvements made by Marcus and Roth, providing insights into computing bounds efficiently.
The authors revisit optimization problems by Kolesnik, Krachkovsky, Marcus, and Roth to enhance the GV bound. They develop numerical procedures and plot curves for constrained systems with various states.
Key concepts include Hamming metric, ball volume calculations, adjacency matrices, power iteration methods, Newton-Raphson iterations, and asymptotic code rates.
The paper offers detailed explanations of computations and optimizations in a mathematical context.
統計資料
In [18], it is mentioned that "the GV bound required considerable computation."
The GV-MR bound improves the usual GV bound in most cases.
For a (3, 2)-SWCC system at δ = 0.1: RGV(0.1) = 0.202.
The GV-MR curve for a (3, 2)-SECC system yields a significantly better lower bound compared to a GV-type bound given in [24].