Browsing by Author "Tan, Vincent Y. F."

Now showing 1 - 2 of 2

Applications of an Exact Formula for the Largest Minimum Distance of Block Codes
(2018-01-01)
Chang, Ling-Hua
;
Wang, Carol
;
Chen, Po-Ning
;
Tan, Vincent Y. F.
;
Han, Yunghsiang S.
An exact information spectrum-type formula for the maximum size of finite length block codes subject to a minimum pairwise distance constraint is presented. This formula can be applied to codes for a broad class of distance measures, which only requires having the minimum value between a point and itself. As revealed by the formula, the largest code size is fully characterized by the information spectrum of the distance between two independent and identically distributed (i.i.d.) random codewords drawn from an optimal distribution. Under an arbitrary uniformly bounded distance measure, the asymptotic largest code rate (in the block length n) attainable for a sequence of (n; M; n delta)-codes is given exactly by the maximum large deviation rate function of the normalized distance between two i.i.d. random codewords.
On the Maximum Size of Block Codes Subject to a Distance Criterion
(2019-06-01)
Chang, Ling-Hua
;
Chen, Po-Ning
;
Tan, Vincent Y. F.
;
Wang, Carol
;
Han, Yunghsiang S.
We establish a general formula for the maximum size of finite length block codes with minimum pairwise distance no less than d. The achievability argument involves an iterative construction of a set of radius-d balls, each centered at a codeword. We demonstrate that the number of such balls that cover the entire code space cannot exceed this maximum size. Our approach can be applied to codes i) with elements over arbitrary code alphabets, and ii) under a broad class of distance measures. Our formula indicates that the maximum code size can be fully characterized by the cumulative distribution function of the distance measure evaluated at two independent and identically distributed random codewords. When the two random codewords assume a uniform distribution over the entire code alphabet, our formula recovers and thus naturally generalizes the Gilbert-Varshamov (GV) lower bound. Finally, we extend our study to the asymptotic setting.