Bit Error Rate Performance of Soft Decision Viterbi Decoding

Yutaka YASUDA; Yasuo HIRATA; Akira OGAWA

Bit Error Rate Performance of Soft Decision Viterbi Decoding

Yutaka YASUDA, Yasuo HIRATA, Akira OGAWA

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Bit error rate (BER) performance of convolutional coding/soft decision Viterbi decoding is investigated theoretically. Firstly, equations are derived to calculate the tight upper bound of the BER performance for the multi-level soft decision with arbitrary threshold spacing, considering the quantized metric used in the Viterbi decoder. Experimental results on the BER performance of a rate 1/2 code with constraint length 7 are shown to demonstrate that the derived equations provide the precise BER performance. Then, the BER performance of various codes is calculated for 4- and 8-level soft decision as well as hard decision and ideal (infinite level) soft decision. The codes examined in this paper cover typical codes with 64 states of rate 1/4 through 3/4 and the rate 1/2 codes with constraint length 3 through 14. From the BER curves obtained for these codes, the coding gain is clarified as a function of coding rate and code constraint length. Main results obtained in this paper are as follows. (1) Among codes with 64 states, rate 1/3 code gives the maximum coding gain. (2) Coding gain of a rate 1/2 code increases as constraint length K becomes large. In the case of 8-level soft decision, for instance, the coding gain of the code with K14 reaches 7.1 dB at BER10^-6, which is close to the maximum coding gain obtained by an infinite constraint length code (estimated to be 7.9 dB).

Publication: IEICE TRANSACTIONS on transactions Vol.E64-E No.11 pp.700-707

Publication Date: 1981/11/25

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Type of Manuscript: PAPER

Category: Transmission Systems

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Yutaka YASUDA
Yasuo HIRATA
Akira OGAWA

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Yutaka YASUDA, Yasuo HIRATA, Akira OGAWA, "Bit Error Rate Performance of Soft Decision Viterbi Decoding" in IEICE TRANSACTIONS on transactions, vol. E64-E, no. 11, pp. 700-707, November 1981, doi: .
Abstract: Bit error rate (BER) performance of convolutional coding/soft decision Viterbi decoding is investigated theoretically. Firstly, equations are derived to calculate the tight upper bound of the BER performance for the multi-level soft decision with arbitrary threshold spacing, considering the quantized metric used in the Viterbi decoder. Experimental results on the BER performance of a rate 1/2 code with constraint length 7 are shown to demonstrate that the derived equations provide the precise BER performance. Then, the BER performance of various codes is calculated for 4- and 8-level soft decision as well as hard decision and ideal (infinite level) soft decision. The codes examined in this paper cover typical codes with 64 states of rate 1/4 through 3/4 and the rate 1/2 codes with constraint length 3 through 14. From the BER curves obtained for these codes, the coding gain is clarified as a function of coding rate and code constraint length. Main results obtained in this paper are as follows. (1) Among codes with 64 states, rate 1/3 code gives the maximum coding gain. (2) Coding gain of a rate 1/2 code increases as constraint length K becomes large. In the case of 8-level soft decision, for instance, the coding gain of the code with K14 reaches 7.1 dB at BER10^-6, which is close to the maximum coding gain obtained by an infinite constraint length code (estimated to be 7.9 dB).
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e64-e_11_700/_p

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@ARTICLE{e64-e_11_700,
author={Yutaka YASUDA, Yasuo HIRATA, Akira OGAWA, },
journal={IEICE TRANSACTIONS on transactions},
title={Bit Error Rate Performance of Soft Decision Viterbi Decoding},
year={1981},
volume={E64-E},
number={11},
pages={700-707},
abstract={Bit error rate (BER) performance of convolutional coding/soft decision Viterbi decoding is investigated theoretically. Firstly, equations are derived to calculate the tight upper bound of the BER performance for the multi-level soft decision with arbitrary threshold spacing, considering the quantized metric used in the Viterbi decoder. Experimental results on the BER performance of a rate 1/2 code with constraint length 7 are shown to demonstrate that the derived equations provide the precise BER performance. Then, the BER performance of various codes is calculated for 4- and 8-level soft decision as well as hard decision and ideal (infinite level) soft decision. The codes examined in this paper cover typical codes with 64 states of rate 1/4 through 3/4 and the rate 1/2 codes with constraint length 3 through 14. From the BER curves obtained for these codes, the coding gain is clarified as a function of coding rate and code constraint length. Main results obtained in this paper are as follows. (1) Among codes with 64 states, rate 1/3 code gives the maximum coding gain. (2) Coding gain of a rate 1/2 code increases as constraint length K becomes large. In the case of 8-level soft decision, for instance, the coding gain of the code with K14 reaches 7.1 dB at BER10^-6, which is close to the maximum coding gain obtained by an infinite constraint length code (estimated to be 7.9 dB).},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - Bit Error Rate Performance of Soft Decision Viterbi Decoding
T2 - IEICE TRANSACTIONS on transactions
SP - 700
EP - 707
AU - Yutaka YASUDA
AU - Yasuo HIRATA
AU - Akira OGAWA
PY - 1981
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E64-E
IS - 11
JA - IEICE TRANSACTIONS on transactions
Y1 - November 1981
AB - Bit error rate (BER) performance of convolutional coding/soft decision Viterbi decoding is investigated theoretically. Firstly, equations are derived to calculate the tight upper bound of the BER performance for the multi-level soft decision with arbitrary threshold spacing, considering the quantized metric used in the Viterbi decoder. Experimental results on the BER performance of a rate 1/2 code with constraint length 7 are shown to demonstrate that the derived equations provide the precise BER performance. Then, the BER performance of various codes is calculated for 4- and 8-level soft decision as well as hard decision and ideal (infinite level) soft decision. The codes examined in this paper cover typical codes with 64 states of rate 1/4 through 3/4 and the rate 1/2 codes with constraint length 3 through 14. From the BER curves obtained for these codes, the coding gain is clarified as a function of coding rate and code constraint length. Main results obtained in this paper are as follows. (1) Among codes with 64 states, rate 1/3 code gives the maximum coding gain. (2) Coding gain of a rate 1/2 code increases as constraint length K becomes large. In the case of 8-level soft decision, for instance, the coding gain of the code with K14 reaches 7.1 dB at BER10^-6, which is close to the maximum coding gain obtained by an infinite constraint length code (estimated to be 7.9 dB).
ER -