The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
A b-symbol read channel é um modelo de canal no qual b símbolos consecutivos são lidos de uma só vez. Como casos especiais, inclui um canal de leitura de pares de símbolos (b=2) e um canal comum (b=1). O limite de empacotamento de esfera, o limite de Gilbert-Varshamov (GV) e o limite GV assintótico para canais de leitura de pares de símbolos são conhecidos por b=1 e 2. Neste artigo, derivamos esses três limites para b-símbolo de leitura de canais com b≥1. A partir da análise do limite VG proposto, confirma-se que a taxa alcançável é mais elevada para bcanais de leitura de símbolos comparados com aqueles de canais comuns com base na métrica de Hamming. Além disso, é mostrado que o valor ótimo de b que maximiza o limite GV assintótico é determinado finitamente dependendo da distância mínima fracionária.
Seunghoan SONG
Osaka University
Toru FUJIWARA
Osaka University
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Seunghoan SONG, Toru FUJIWARA, "Sphere Packing Bound and Gilbert-Varshamov Bound for b-Symbol Read Channels" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 11, pp. 1915-1924, November 2018, doi: 10.1587/transfun.E101.A.1915.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.1915/_p
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@ARTICLE{e101-a_11_1915,
author={Seunghoan SONG, Toru FUJIWARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Sphere Packing Bound and Gilbert-Varshamov Bound for b-Symbol Read Channels},
year={2018},
volume={E101-A},
number={11},
pages={1915-1924},
abstract={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.},
keywords={},
doi={10.1587/transfun.E101.A.1915},
ISSN={1745-1337},
month={November},}
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TY - JOUR
TI - Sphere Packing Bound and Gilbert-Varshamov Bound for b-Symbol Read Channels
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1915
EP - 1924
AU - Seunghoan SONG
AU - Toru FUJIWARA
PY - 2018
DO - 10.1587/transfun.E101.A.1915
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2018
AB - 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.
ER -