| 21. |
- Alvarado, A., et al.
(författare)
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High-SNR Asymptotics of Mutual Information for Discrete Constellations With Applications to BICM
- 2014
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 60:2, s. 1061-1076
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Tidskriftsartikel (refereegranskat)abstract
- Asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white Gaussian noise channel are presented in the limit as the signal-to-noise ratio (SNR) tends to infinity. Asymptotic expressions of the symbol-error probability (SEP) and the minimum mean-square error (MMSE) achieved by estimating the channel input given the channel output are also developed. It is shown that for any input distribution, the conditional entropy of the channel input given the output, MMSE, and SEP have an asymptotic behavior proportional to the Gaussian Q-function. The argument of the Q-function depends only on the minimum Euclidean distance (MED) of the constellation and the SNR, and the proportionality constants are functions of the MED and the probabilities of the pairs of constellation points at MED. The developed expressions are then generalized to study the high-SNR behavior of the generalized mutual information (GMI) for bit-interleaved coded modulation (BICM). By means of these asymptotic expressions, the long-standing conjecture that Gray codes are the binary labelings that maximize the BICM-GMI at high SNR is proven. It is further shown that for any equally spaced constellation whose size is a power of two, there always exists an anti-Gray code giving the lowest BICM-GMI at high SNR.
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| 22. |
- Alvarado, Alex, 1982, et al.
(författare)
-
High SNR Bounds for the BICM Capacity
- 2011
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Ingår i: IEEE Information Theory Workshop ITW 2011, Paraty, Brazil. ; , s. 360-364
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Konferensbidrag (refereegranskat)abstract
- In this paper, different aspects of the bit-interleaved coded modulation (BICM) capacity for the Gaussian channel are analyzed. Analytical bounds for the BICM capacity are developed. These bounds suggest that the BICM capacity at high signal-to-noise ration (SNR) is determined by the multiplicity of the minimum Euclidean distance over all the subconstellations generated by the mapper. Based on this observation, we conjecture that for any constellation, the highest BICM capacity at high SNR is always obtained by a Gray code, if one exists. Ready-to-use expressions based on Gauss--Hermite quadratures to compute the coded modulation and BICM capacities for any SNR are also presented. Using these expressions, it is shown that the BICM capacity is in general a nonconvex, nonconcave function of the input bit distribution. For 8PAM and 8PSK, there exist 12 and 7 classes of mappings, respectively, with equivalent high-SNR behavior, of which the best class comprises all Gray codes.
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| 23. |
- Alvarado, Alex, 1982, et al.
(författare)
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On BICM-ID with Multiple Interleavers
- 2010
-
Ingår i: IEEE Communications Letters. - 1558-2558 .- 1089-7798. ; 14:9, s. 785-787
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Tidskriftsartikel (refereegranskat)abstract
- In this letter, we study the performance of BICM-ID with multiple interleavers (BICM-ID-M) in terms of bit-error rate (BER), and show that BICM-ID-M is well-suited to exploit the unequal error protection (UEP) caused by the binary labeling. We show that BICM-ID-M should always be the preferred alternative for BICM-ID and that the gains obtained appear even for the simplest configuration (0.5-0.75 dB for a BER of 10-7). It is found that conventional design paradigms such as maximizing the free distance of the code should be modified.
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| 24. |
- Alvarado, Alex, 1982, et al.
(författare)
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On BICM receivers for TCM transmission
- 2011
-
Ingår i: IEEE Transactions on Communications. - 0090-6778 .- 1558-0857. ; 59:10, s. 2692-2702
-
Tidskriftsartikel (refereegranskat)abstract
- Recent results have shown that the performance of bit-interleaved coded modulation (BICM) using convolutional codes in nonfading channels can be significantly improved when the interleaver takes a trivial form (BICM-T), i.e., when it does not interleave the bits at all. In this paper, we give a formal explanation for these results and show that BICM-T is, in fact, the combination of a TCM transmitter and a BICM receiver. To predict the performance of BICM-T, a new type of distance spectrum for convolutional codes is introduced, analytical bounds based on this spectrum are developed, and asymptotic approximations are presented. It is shown that the free Hamming distance of the code is not the relevant optimization criterion for BICM-T. Asymptotically optimal convolutional codes for different constraint lengths are tabulated and BICM-T is shown to offer asymptotic gains of about 2 dB over traditional BICM designs based on random interleavers. The asymptotic gains over uncoded transmission are found to be the same as those obtained by Ungerboeck's one-dimensional trellis-coded modulation (1D-TCM), and therefore, in nonfading channels, BICM-T is shown to be as good as 1D-TCM.
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| 25. |
- Alvarado, Alex, 1982, et al.
(författare)
-
On Optimal TCM Encoders
- 2013
-
Ingår i: IEEE Transactions on Communications. - 0090-6778 .- 1558-0857. ; 61:6, s. 2178 - 2189
-
Tidskriftsartikel (refereegranskat)abstract
- An asymptotically optimal trellis-coded modulation (TCM) encoder requires the joint design of the encoder and the binary labeling of the constellation. Since analytical approaches are unknown, the only available solution is to perform an exhaustive search over the encoder and the labeling. For large constellation sizes and/or many encoder states, however, an exhaustive search is unfeasible. Traditional TCM designs overcome this problem by using a labeling that follows the set-partitioning principle and by performing an exhaustive search over the encoders. In this paper we study binary labelings for TCM and show how they can be grouped into classes, which considerably reduces the search space in a joint design. For $8$-ary constellations, the number of different binary labelings that must be tested is reduced from $8!=40320$ to $240$. For the particular case of an $8$-ary pulse amplitude modulation constellation, this number is further reduced to $120$ and for $8$-ary phase shift keying to only $30$. An algorithm to generate one labeling in each class is also introduced. Asymptotically optimal TCM encoders are tabulated which are up to $0.3$~dB better than the previously best known encoders.
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| 26. |
- Alvarado, Alex, 1982, et al.
(författare)
-
On the Equivalence of TCM Encoders
- 2012
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Ingår i: 2012 IEEE International Symposium on Information Theory, ISIT 2012. Cambridge, MA, 1 - 6 July 2012. - 9781467325790 ; , s. 2401-2405
-
Konferensbidrag (refereegranskat)abstract
- Optimal trellis-coded modulation (TCM) schemes are obtained by jointly designing the convolutional encoder and the binary labeling of the constellation. Unfortunately this approach is infeasible for large encoder memories or constellation sizes. Traditional TCM designs circumvent this problem by using a labeling that follows the set-partitioning principle and by performing an exhaustive search over the encoders. Therefore, traditional TCM schemes are not necessarily optimal. In this paper, we study binary labelings for TCM and show how they can be grouped into classes, which considerably reduces the search space in a joint design. For the particular case of 8-ary modulation the search space is reduced from 40320 to 240. Using this classification, we formally prove that for any channel it is always possible to design a TCM system based on the binary-reflected Gray code with identical performance to the one proposed by Ungerboeck in 1982. Moreover, the classification is used to tabulate asymptotically optimal TCM schemes.
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| 27. |
- Alvarado, Alex, 1982, et al.
(författare)
-
On the performance of BICM with trivial interleavers in nonfading channels
- 2011
-
Ingår i: IEEE International Conference on Communications ICC 2011. - : IEEE. - 1550-3607. - 9781612842332
-
Konferensbidrag (refereegranskat)abstract
- Recent results have shown that the performance of bit-interleaved coded modulation (BICM) using convolutional codes in nonfading channels can be greatly improved if the bit-level interleaver takes a trivial form (BICM-T), i.e., if it does not interleave the bits at all. The reported gains reach a few decibels and are obtained using a less complex BICM system. In this paper, we give a formal explanation for these results and show that BICM-T is in fact the combination of a TCM transmitter and a BICM receiver. Analytical bounds that predict the performance of BICM-T are developed and a new type of distance spectrum for the convolutional code is introduced.
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| 28. |
- Beygi, Lotfollah, 1977, et al.
(författare)
-
A Discrete-Time Model for Uncompensated Single-Channel Fiber-Optical Links
- 2012
-
Ingår i: IEEE Transactions on Communications. - 0090-6778 .- 1558-0857. ; 60:11, s. 3440-3450
-
Tidskriftsartikel (refereegranskat)abstract
- An analytical discrete-time model is introduced for single-wavelength polarization multiplexed nonlinear fiber-optical channels based on the symmetrized split-step Fourier method (SSFM). According to this model, for high enough symbol rates, a fiber-optic link can be described as a linear dispersive channel with additive white Gaussian noise (AWGN) and a complex scaling. The variance of this AWGN noise and the attenuation are computed analytically as a function of input power and channel parameters. The results illustrate a cubic growth of the noise variance with input power. Moreover, the cross effect between the two polarizations and the interaction of amplifier noise and the transmitted signal due to the nonlinear Kerr effect are described. In particular, it is found that the channel noise variance in one polarization is affected twice as much by the transmitted power in that polarization than by the transmitted power in the orthogonal polarization.The effect of pulse shaping is also investigated through numerical simulations. Finally, it is shown that the analytical performance results based on the new model are in close agreement with numerical results obtained using the SSFM for a symbol rate of 28 Gbaud and above.
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| 29. |
- Beygi, Lotfollah, 1977, et al.
(författare)
-
A novel multilevel coded modulation scheme for fiber optical channel with nonlinear phase noise
- 2010
-
Ingår i: Proc. Global Communications Conference, Miami, FL. - 9781424456383
-
Konferensbidrag (refereegranskat)abstract
- A multilevel coded modulation (MLCM) system in the presence of nonlinear phase noise for fiber optical communication is introduced. The proposed scheme exploits a 16-point ring constellation with nonlinear post compensation of the self phase modulation produced via the Kerr effect. A new set partitioning based on the Ungerboeck approach is introduced to maintain unequal error protection in amplitude and phase direction. The rate allocation for the MLCM component codes for different fiber lengths and transmit powers are done numerically. Simulation results show that the proposed MLCM system provides up to 2 dB gain over a forward error correcting scheme for a block error rates around 10-9, with the same overhead (7%) and complexity. ©2010 IEEE.
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| 30. |
- Beygi, Lotfollah, 1977, et al.
(författare)
-
A novel rate allocation method for multilevel coded modulation
- 2010
-
Ingår i: IEEE International Symposium on Information Theory - Proceedings. - 2157-8095. - 9781424469604 ; , s. 1983-1987
-
Konferensbidrag (refereegranskat)abstract
- We present a new rate allocation scheme for multilevelcoded modulation based on the minimization of the totalblock error rate (BLER). The proposed method uses affine codecomponents and hard decision multistage decoding. Exhaustivesearch for the rate allocation which minimizes the total BLERjustifies the near-optimum performance of the introduced methodin moderate to high SNRs. Compared to previous approaches thisnew rate allocation scheme can improve the performance of thesystem by 1 dB at BLER = 10−6 for 16-QAM with Ungerboeck setpartitioning. Interestingly, our results indicate that the optimumrate allocation is a function of the SNR. Finally, the performanceof some specific codes are evaluated by simulation and unionbounds to verify the theoretical results.
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