An encoder of a trellis coded modulation (TCM) is composed of a linear convolutional encoder followed by a mapper to channel signals. A new condition, under which the performance evaluation of the TCM is possible based on the 2ν state error state transition diagram, is proposed, where ν is the number of delay elements in the convolutional encoder. There have been proposed three similar methods. This paper points out the restriction of the previous methods, and proposes a new method. The condition, under which the previous method is useful, is called nuiformity, such as, the error weight profile is independent from the encoder state. When uniformity does not hold, we discuss to divide an error state into substates based on the coset decomposition of output vectors of the convolutional encoder. The coset is determined by the vector called coset selector. If the condition defined as equal dividing holds, the subdivided states can be merged and the performance can be evaluated based on the 2ν state transition diagram, even for the codes without uniformity. When the row rank of the transformation matrix, from the input vector of the encoder to the coset selector vector, is full, the equal dividing condition holds under the assumption of equally probable i.i.d. (independently identically distributed) input sequence. For TCM schemes without uniformity (in the case, previous methods can not be applied), upper bounds of the bit error rate are evaluated by the proposed method and compared with the simulation results. The difference is less than 10% in the range of bet error rate
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Haruo OGIWARA, Kazuo OOHIRA, "Performance Evaluation Method of Trellis Coded Modulation Scheme without Uniformity" in IEICE TRANSACTIONS on Fundamentals,
vol. E77-A, no. 8, pp. 1267-1273, August 1994, doi: .
Abstract: An encoder of a trellis coded modulation (TCM) is composed of a linear convolutional encoder followed by a mapper to channel signals. A new condition, under which the performance evaluation of the TCM is possible based on the 2ν state error state transition diagram, is proposed, where ν is the number of delay elements in the convolutional encoder. There have been proposed three similar methods. This paper points out the restriction of the previous methods, and proposes a new method. The condition, under which the previous method is useful, is called nuiformity, such as, the error weight profile is independent from the encoder state. When uniformity does not hold, we discuss to divide an error state into substates based on the coset decomposition of output vectors of the convolutional encoder. The coset is determined by the vector called coset selector. If the condition defined as equal dividing holds, the subdivided states can be merged and the performance can be evaluated based on the 2ν state transition diagram, even for the codes without uniformity. When the row rank of the transformation matrix, from the input vector of the encoder to the coset selector vector, is full, the equal dividing condition holds under the assumption of equally probable i.i.d. (independently identically distributed) input sequence. For TCM schemes without uniformity (in the case, previous methods can not be applied), upper bounds of the bit error rate are evaluated by the proposed method and compared with the simulation results. The difference is less than 10% in the range of bet error rate
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e77-a_8_1267/_p
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@ARTICLE{e77-a_8_1267,
author={Haruo OGIWARA, Kazuo OOHIRA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Performance Evaluation Method of Trellis Coded Modulation Scheme without Uniformity},
year={1994},
volume={E77-A},
number={8},
pages={1267-1273},
abstract={An encoder of a trellis coded modulation (TCM) is composed of a linear convolutional encoder followed by a mapper to channel signals. A new condition, under which the performance evaluation of the TCM is possible based on the 2ν state error state transition diagram, is proposed, where ν is the number of delay elements in the convolutional encoder. There have been proposed three similar methods. This paper points out the restriction of the previous methods, and proposes a new method. The condition, under which the previous method is useful, is called nuiformity, such as, the error weight profile is independent from the encoder state. When uniformity does not hold, we discuss to divide an error state into substates based on the coset decomposition of output vectors of the convolutional encoder. The coset is determined by the vector called coset selector. If the condition defined as equal dividing holds, the subdivided states can be merged and the performance can be evaluated based on the 2ν state transition diagram, even for the codes without uniformity. When the row rank of the transformation matrix, from the input vector of the encoder to the coset selector vector, is full, the equal dividing condition holds under the assumption of equally probable i.i.d. (independently identically distributed) input sequence. For TCM schemes without uniformity (in the case, previous methods can not be applied), upper bounds of the bit error rate are evaluated by the proposed method and compared with the simulation results. The difference is less than 10% in the range of bet error rate
keywords={},
doi={},
ISSN={},
month={August},}
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TY - JOUR
TI - Performance Evaluation Method of Trellis Coded Modulation Scheme without Uniformity
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1267
EP - 1273
AU - Haruo OGIWARA
AU - Kazuo OOHIRA
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E77-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 1994
AB - An encoder of a trellis coded modulation (TCM) is composed of a linear convolutional encoder followed by a mapper to channel signals. A new condition, under which the performance evaluation of the TCM is possible based on the 2ν state error state transition diagram, is proposed, where ν is the number of delay elements in the convolutional encoder. There have been proposed three similar methods. This paper points out the restriction of the previous methods, and proposes a new method. The condition, under which the previous method is useful, is called nuiformity, such as, the error weight profile is independent from the encoder state. When uniformity does not hold, we discuss to divide an error state into substates based on the coset decomposition of output vectors of the convolutional encoder. The coset is determined by the vector called coset selector. If the condition defined as equal dividing holds, the subdivided states can be merged and the performance can be evaluated based on the 2ν state transition diagram, even for the codes without uniformity. When the row rank of the transformation matrix, from the input vector of the encoder to the coset selector vector, is full, the equal dividing condition holds under the assumption of equally probable i.i.d. (independently identically distributed) input sequence. For TCM schemes without uniformity (in the case, previous methods can not be applied), upper bounds of the bit error rate are evaluated by the proposed method and compared with the simulation results. The difference is less than 10% in the range of bet error rate
ER -