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   Vol.E101-A   No.11   pp.1915-1924
Publication Date: 2018/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.1915
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,  

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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.