Multidimensional Hybrid Modulations for Ultrahigh-Speed Optical Transport
From Shanon's theory, we know that information capacity is a logarithmic function of signal-to-noise ratio (SNR) but a linear function of the number of dimensions. By increasing the number of dimensions <formula formulatype="inline"><tex Notation="TeX">$D$</te...
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| Format: | Article |
| Language: | English |
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IEEE
2011-01-01
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| Series: | IEEE Photonics Journal |
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| Online Access: | https://ieeexplore.ieee.org/document/6059467/ |
| _version_ | 1819008850801459200 |
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| author | Ivan B. Djordjevic Lei Xu Ting Wang |
| author_facet | Ivan B. Djordjevic Lei Xu Ting Wang |
| author_sort | Ivan B. Djordjevic |
| collection | DOAJ |
| description | From Shanon's theory, we know that information capacity is a logarithmic function of signal-to-noise ratio (SNR) but a linear function of the number of dimensions. By increasing the number of dimensions <formula formulatype="inline"><tex Notation="TeX">$D$</tex></formula>, we can dramatically improve the spectral efficiency. At the same time, in <formula formulatype="inline"><tex Notation="TeX">$D$</tex></formula>-dimensional space <formula formulatype="inline"> <tex Notation="TeX">$(D\ >\ 2)$</tex></formula>, for the same average symbol energy, we can increase the Euclidean distance between signal constellation points compared with the conventional in-phase (I)/quadrature (Q) 2-D signal space. The 4-D space, with two phase coordinates per polarization, has already been intensively studied. To satisfy the ever-increasing bandwidth demands, in this paper, we propose the <formula formulatype="inline"><tex Notation="TeX">$D$</tex> </formula>-dimensional signaling <formula formulatype="inline"><tex Notation="TeX">$(D\ >\ 4)$</tex></formula> by employing all available degrees of freedom for transmission over a single carrier including amplitude, phase, polarization, and orbital angular momentum (OAM). The proposed modulation scheme can be called hybrid <formula formulatype="inline"><tex Notation="TeX">$D$</tex></formula>-dimensional modulation as it employs all available degrees of freedom. The proposed hybrid 8-D coded-modulation scheme outperforms its 4-D counterpart by 3.97 dB at a bit error rate (BER) of <formula formulatype="inline"><tex Notation="TeX">$10^{-8}$</tex></formula> while outperforming its corresponding polarization-division-multiplexed (PDM) iterative polar quantization (IPQ)-based counterpart by even a larger margin of 6.41 dB (at the same BER). The improvement of the proposed scheme for two amplitude levels per dimension and <formula formulatype="inline"><tex Notation="TeX">$D = 8$</tex></formula> over conventional PDM 64-quadrature amplitude modulation (QAM) is indeed a striking 8.28 dB at a BER of <formula formulatype="inline"><tex Notation="TeX"> $2 \times 10^{-8}$</tex></formula>. |
| first_indexed | 2024-12-21T00:47:02Z |
| format | Article |
| id | doaj.art-e433bed7282d4f3bb8d307ffe1b67fea |
| institution | Directory Open Access Journal |
| issn | 1943-0655 |
| language | English |
| last_indexed | 2024-12-21T00:47:02Z |
| publishDate | 2011-01-01 |
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| spelling | doaj.art-e433bed7282d4f3bb8d307ffe1b67fea2022-12-21T19:21:30ZengIEEEIEEE Photonics Journal1943-06552011-01-01361030103810.1109/JPHOT.2011.21733276059467Multidimensional Hybrid Modulations for Ultrahigh-Speed Optical TransportIvan B. Djordjevic0Lei Xu1Ting Wang2<formula formulatype="inline"><tex Notation="TeX">$^{1}$</tex></formula>Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ, USA<formula formulatype="inline"><tex Notation="TeX">$^{2}$</tex></formula>NEC Laboratories America, Inc., Princeton, NJ, USANEC Laboratories America, Inc., Princeton, NJ, USAFrom Shanon's theory, we know that information capacity is a logarithmic function of signal-to-noise ratio (SNR) but a linear function of the number of dimensions. By increasing the number of dimensions <formula formulatype="inline"><tex Notation="TeX">$D$</tex></formula>, we can dramatically improve the spectral efficiency. At the same time, in <formula formulatype="inline"><tex Notation="TeX">$D$</tex></formula>-dimensional space <formula formulatype="inline"> <tex Notation="TeX">$(D\ >\ 2)$</tex></formula>, for the same average symbol energy, we can increase the Euclidean distance between signal constellation points compared with the conventional in-phase (I)/quadrature (Q) 2-D signal space. The 4-D space, with two phase coordinates per polarization, has already been intensively studied. To satisfy the ever-increasing bandwidth demands, in this paper, we propose the <formula formulatype="inline"><tex Notation="TeX">$D$</tex> </formula>-dimensional signaling <formula formulatype="inline"><tex Notation="TeX">$(D\ >\ 4)$</tex></formula> by employing all available degrees of freedom for transmission over a single carrier including amplitude, phase, polarization, and orbital angular momentum (OAM). The proposed modulation scheme can be called hybrid <formula formulatype="inline"><tex Notation="TeX">$D$</tex></formula>-dimensional modulation as it employs all available degrees of freedom. The proposed hybrid 8-D coded-modulation scheme outperforms its 4-D counterpart by 3.97 dB at a bit error rate (BER) of <formula formulatype="inline"><tex Notation="TeX">$10^{-8}$</tex></formula> while outperforming its corresponding polarization-division-multiplexed (PDM) iterative polar quantization (IPQ)-based counterpart by even a larger margin of 6.41 dB (at the same BER). The improvement of the proposed scheme for two amplitude levels per dimension and <formula formulatype="inline"><tex Notation="TeX">$D = 8$</tex></formula> over conventional PDM 64-quadrature amplitude modulation (QAM) is indeed a striking 8.28 dB at a BER of <formula formulatype="inline"><tex Notation="TeX"> $2 \times 10^{-8}$</tex></formula>.https://ieeexplore.ieee.org/document/6059467/Multimode fibers (MMFs)hybrid modulationslow-density parity-check (LDPC) codescoded-modulation |
| spellingShingle | Ivan B. Djordjevic Lei Xu Ting Wang Multidimensional Hybrid Modulations for Ultrahigh-Speed Optical Transport IEEE Photonics Journal Multimode fibers (MMFs) hybrid modulations low-density parity-check (LDPC) codes coded-modulation |
| title | Multidimensional Hybrid Modulations for Ultrahigh-Speed Optical Transport |
| title_full | Multidimensional Hybrid Modulations for Ultrahigh-Speed Optical Transport |
| title_fullStr | Multidimensional Hybrid Modulations for Ultrahigh-Speed Optical Transport |
| title_full_unstemmed | Multidimensional Hybrid Modulations for Ultrahigh-Speed Optical Transport |
| title_short | Multidimensional Hybrid Modulations for Ultrahigh-Speed Optical Transport |
| title_sort | multidimensional hybrid modulations for ultrahigh speed optical transport |
| topic | Multimode fibers (MMFs) hybrid modulations low-density parity-check (LDPC) codes coded-modulation |
| url | https://ieeexplore.ieee.org/document/6059467/ |
| work_keys_str_mv | AT ivanbdjordjevic multidimensionalhybridmodulationsforultrahighspeedopticaltransport AT leixu multidimensionalhybridmodulationsforultrahighspeedopticaltransport AT tingwang multidimensionalhybridmodulationsforultrahighspeedopticaltransport |