For Full-Text PDF, please login, if you are a member of IEICE,|
or go to Pay Per View on menu list, if you are a nonmember of IEICE.
Sphere Packing Bound and Gilbert-Varshamov Bound for b-Symbol Read Channels
Seunghoan SONG Toru FUJIWARA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2018/11/01
Online ISSN: 1745-1337
Type of Manuscript: PAPER
Category: Coding Theory
symbol-pair read channel, b-symbol read channel, sphere packing bound, Gilbert-Varshamov (G-V) bound, asymptotic code bound,
Full Text: PDF(812.8KB)
>>Buy this Article
A b-symbol read channel is a channel model in which b consecutive symbols are read at once. As special cases, it includes a symbol-pair read channel (b=2) and an ordinary channel (b=1). The sphere packing bound, the Gilbert-Varshamov (G-V) bound, and the asymptotic G-V bound for symbol-pair read channels are known for b=1 and 2. In this paper, we derive these three bounds for b-symbol read channels with b≥1. From analysis of the proposed G-V bound, it is confirmed that the achievable rate is higher for b-symbol read channels compared with those for ordinary channels based on the Hamming metric. Furthermore, it is shown that the optimal value of b that maximizes the asymptotic G-V bound is finitely determined depending on the fractional minimum distance.