On Trellis Structure of LUEP Block Codes and a Class of UEP QPSK Block Modulation Codes

Robert MORELOS-ZARAGOZA

On Trellis Structure of LUEP Block Codes and a Class of UEP QPSK Block Modulation Codes

Robert MORELOS-ZARAGOZA

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Recently there has been considerable interest in coded modulation schemes that offer multiple levels of error protection. That is, constructions of (block or convolutional) modulation codes in which signal sequences associated with some message symbols are separated by a squared Euclidean distance that is larger than the minimum squared Euclidean distance (MSED) of the code. In this paper, the trellis structure of linear unequal-error-protection (LUEP) codes is analyzed. First, it is shown that LUEP codes have trellises that can be expressed as a direct product of trellises of subcodes or clouds. This particular trellis structure is a result of the cloud structure of LUEP codes in general. A direct consequence of this property of LUEP codes is that searching for trellises with parallel structure for a block modulation code may be useful not only in analyzing its structure and in simplifying its decoding, but also in determining its UEP capabilities. A basic 3-level 8-PSK block modulation code is analyzed under this new perspective, and shown to offer two levels of error protection. To illustrate the trellis structure of an LUEP code, we analyze a trellis diagram for an extended (64,24) BCH code, which is a two-level LUEP code. Furthermore, we introduce a family of LUEP codes based on the |||-construction, using Reed-Muller (RM) codes as component codes. LUEP codes in this family have the advantage of having a well known trellis structure. Their application in constructing LUEP-QPSK modulation codes is presented, and their error performance over an AWGN channel examined.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E77-A No.8 pp.1261-1266

Publication Date: 1994/08/25

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Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)

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Robert MORELOS-ZARAGOZA, "On Trellis Structure of LUEP Block Codes and a Class of UEP QPSK Block Modulation Codes" in IEICE TRANSACTIONS on Fundamentals, vol. E77-A, no. 8, pp. 1261-1266, August 1994, doi: .
Abstract: Recently there has been considerable interest in coded modulation schemes that offer multiple levels of error protection. That is, constructions of (block or convolutional) modulation codes in which signal sequences associated with some message symbols are separated by a squared Euclidean distance that is larger than the minimum squared Euclidean distance (MSED) of the code. In this paper, the trellis structure of linear unequal-error-protection (LUEP) codes is analyzed. First, it is shown that LUEP codes have trellises that can be expressed as a direct product of trellises of subcodes or clouds. This particular trellis structure is a result of the cloud structure of LUEP codes in general. A direct consequence of this property of LUEP codes is that searching for trellises with parallel structure for a block modulation code may be useful not only in analyzing its structure and in simplifying its decoding, but also in determining its UEP capabilities. A basic 3-level 8-PSK block modulation code is analyzed under this new perspective, and shown to offer two levels of error protection. To illustrate the trellis structure of an LUEP code, we analyze a trellis diagram for an extended (64,24) BCH code, which is a two-level LUEP code. Furthermore, we introduce a family of LUEP codes based on the |||-construction, using Reed-Muller (RM) codes as component codes. LUEP codes in this family have the advantage of having a well known trellis structure. Their application in constructing LUEP-QPSK modulation codes is presented, and their error performance over an AWGN channel examined.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e77-a_8_1261/_p

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@ARTICLE{e77-a_8_1261,
author={Robert MORELOS-ZARAGOZA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On Trellis Structure of LUEP Block Codes and a Class of UEP QPSK Block Modulation Codes},
year={1994},
volume={E77-A},
number={8},
pages={1261-1266},
abstract={Recently there has been considerable interest in coded modulation schemes that offer multiple levels of error protection. That is, constructions of (block or convolutional) modulation codes in which signal sequences associated with some message symbols are separated by a squared Euclidean distance that is larger than the minimum squared Euclidean distance (MSED) of the code. In this paper, the trellis structure of linear unequal-error-protection (LUEP) codes is analyzed. First, it is shown that LUEP codes have trellises that can be expressed as a direct product of trellises of subcodes or clouds. This particular trellis structure is a result of the cloud structure of LUEP codes in general. A direct consequence of this property of LUEP codes is that searching for trellises with parallel structure for a block modulation code may be useful not only in analyzing its structure and in simplifying its decoding, but also in determining its UEP capabilities. A basic 3-level 8-PSK block modulation code is analyzed under this new perspective, and shown to offer two levels of error protection. To illustrate the trellis structure of an LUEP code, we analyze a trellis diagram for an extended (64,24) BCH code, which is a two-level LUEP code. Furthermore, we introduce a family of LUEP codes based on the |||-construction, using Reed-Muller (RM) codes as component codes. LUEP codes in this family have the advantage of having a well known trellis structure. Their application in constructing LUEP-QPSK modulation codes is presented, and their error performance over an AWGN channel examined.},
keywords={},
doi={},
ISSN={},
month={August},}

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TY - JOUR
TI - On Trellis Structure of LUEP Block Codes and a Class of UEP QPSK Block Modulation Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1261
EP - 1266
AU - Robert MORELOS-ZARAGOZA
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E77-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 1994
AB - Recently there has been considerable interest in coded modulation schemes that offer multiple levels of error protection. That is, constructions of (block or convolutional) modulation codes in which signal sequences associated with some message symbols are separated by a squared Euclidean distance that is larger than the minimum squared Euclidean distance (MSED) of the code. In this paper, the trellis structure of linear unequal-error-protection (LUEP) codes is analyzed. First, it is shown that LUEP codes have trellises that can be expressed as a direct product of trellises of subcodes or clouds. This particular trellis structure is a result of the cloud structure of LUEP codes in general. A direct consequence of this property of LUEP codes is that searching for trellises with parallel structure for a block modulation code may be useful not only in analyzing its structure and in simplifying its decoding, but also in determining its UEP capabilities. A basic 3-level 8-PSK block modulation code is analyzed under this new perspective, and shown to offer two levels of error protection. To illustrate the trellis structure of an LUEP code, we analyze a trellis diagram for an extended (64,24) BCH code, which is a two-level LUEP code. Furthermore, we introduce a family of LUEP codes based on the |||-construction, using Reed-Muller (RM) codes as component codes. LUEP codes in this family have the advantage of having a well known trellis structure. Their application in constructing LUEP-QPSK modulation codes is presented, and their error performance over an AWGN channel examined.
ER -