Channel decomposition for multilevel codes over multilevel and partial erasure channels

Carolyn Mayer, Kathryn Haymaker, Christine A. Kelley

Research output: Contribution to journalArticle

Abstract

We introduce the Multilevel Erasure Channel (MEC) for binary extension field alphabets. The channel model is motivated by applications such as non-volatile multilevel read storage channels. Like the recently proposed q-ary partial erasure channel (QPEC), the MEC is designed to capture partial erasures. The partial erasures addressed by the MEC are determined by erasures at the bit level of the q-ary symbol representation. In this paper we derive the channel capacity of the MEC and give a multistage decoding scheme on the MEC using binary codes. We also present a low complexity multistage p-ary decoding strategy for codes on the QPEC when q = pk. We show that for appropriately chosen component codes, capacity on the MEC and QPEC may be achieved.

Original languageEnglish (US)
Pages (from-to)151-168
Number of pages18
JournalAdvances in Mathematics of Communications
Volume12
Issue number1
DOIs
StatePublished - Feb 2018

Fingerprint

Decoding
Decomposition
Partial
Decompose
Binary codes
Channel capacity
Channel Capacity
Field extension
Channel Model
Binary Code
Low Complexity
Binary

Keywords

  • Multilevel codes
  • Multistage decoding
  • Partial erasure channels
  • Storage channels

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computer Networks and Communications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Channel decomposition for multilevel codes over multilevel and partial erasure channels. / Mayer, Carolyn; Haymaker, Kathryn; Kelley, Christine A.

In: Advances in Mathematics of Communications, Vol. 12, No. 1, 02.2018, p. 151-168.

Research output: Contribution to journalArticle

@article{c0d90b2aa636459dbc43aeb48cdaa646,
title = "Channel decomposition for multilevel codes over multilevel and partial erasure channels",
abstract = "We introduce the Multilevel Erasure Channel (MEC) for binary extension field alphabets. The channel model is motivated by applications such as non-volatile multilevel read storage channels. Like the recently proposed q-ary partial erasure channel (QPEC), the MEC is designed to capture partial erasures. The partial erasures addressed by the MEC are determined by erasures at the bit level of the q-ary symbol representation. In this paper we derive the channel capacity of the MEC and give a multistage decoding scheme on the MEC using binary codes. We also present a low complexity multistage p-ary decoding strategy for codes on the QPEC when q = pk. We show that for appropriately chosen component codes, capacity on the MEC and QPEC may be achieved.",
keywords = "Multilevel codes, Multistage decoding, Partial erasure channels, Storage channels",
author = "Carolyn Mayer and Kathryn Haymaker and Kelley, {Christine A.}",
year = "2018",
month = "2",
doi = "10.3934/amc.2018010",
language = "English (US)",
volume = "12",
pages = "151--168",
journal = "Advances in Mathematics of Communications",
issn = "1930-5346",
publisher = "American Institute of Mathematical Sciences",
number = "1",

}

TY - JOUR

T1 - Channel decomposition for multilevel codes over multilevel and partial erasure channels

AU - Mayer, Carolyn

AU - Haymaker, Kathryn

AU - Kelley, Christine A.

PY - 2018/2

Y1 - 2018/2

N2 - We introduce the Multilevel Erasure Channel (MEC) for binary extension field alphabets. The channel model is motivated by applications such as non-volatile multilevel read storage channels. Like the recently proposed q-ary partial erasure channel (QPEC), the MEC is designed to capture partial erasures. The partial erasures addressed by the MEC are determined by erasures at the bit level of the q-ary symbol representation. In this paper we derive the channel capacity of the MEC and give a multistage decoding scheme on the MEC using binary codes. We also present a low complexity multistage p-ary decoding strategy for codes on the QPEC when q = pk. We show that for appropriately chosen component codes, capacity on the MEC and QPEC may be achieved.

AB - We introduce the Multilevel Erasure Channel (MEC) for binary extension field alphabets. The channel model is motivated by applications such as non-volatile multilevel read storage channels. Like the recently proposed q-ary partial erasure channel (QPEC), the MEC is designed to capture partial erasures. The partial erasures addressed by the MEC are determined by erasures at the bit level of the q-ary symbol representation. In this paper we derive the channel capacity of the MEC and give a multistage decoding scheme on the MEC using binary codes. We also present a low complexity multistage p-ary decoding strategy for codes on the QPEC when q = pk. We show that for appropriately chosen component codes, capacity on the MEC and QPEC may be achieved.

KW - Multilevel codes

KW - Multistage decoding

KW - Partial erasure channels

KW - Storage channels

UR - http://www.scopus.com/inward/record.url?scp=85047184606&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047184606&partnerID=8YFLogxK

U2 - 10.3934/amc.2018010

DO - 10.3934/amc.2018010

M3 - Article

AN - SCOPUS:85047184606

VL - 12

SP - 151

EP - 168

JO - Advances in Mathematics of Communications

JF - Advances in Mathematics of Communications

SN - 1930-5346

IS - 1

ER -