| 1. |
- Agrell, Erik, 1965, et al.
(författare)
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Achieving the Shannon Limit with Probabilistically Shaped BICM
- 2012
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Ingår i: IEEE International Symposium on Information Theory - Proceedings. - 2157-8095. - 9781467325806 ; , s. 2421-2425
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Konferensbidrag (refereegranskat)abstract
- Probabilistic shaping for bit-interleaved coded modulation (BICM) systems at low signal-to-noise ratio (SNR) is investigated. Using known results for BICM systems with a uniform input distribution, the combinations of input alphabet, input distribution, and binary labeling that achieve the Shannon limit -1.59 dB are fully characterized. It is found that a BICM system achieves the Shannon limit at low SNR if and only if it can be represented as a zero-mean linear projection of a hypercube, which is the same condition as for uniform input distributions. Hence, probabilistic shaping offers no extra degrees of freedom to optimize the low-SNR mutual information of BICM systems, in addition to what is provided by geometrical shaping.
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| 2. |
- Agrell, Erik, 1965, et al.
(författare)
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Capacity of a nonlinear optical channel with finite memory
- 2014
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Ingår i: Journal of Lightwave Technology. - 0733-8724 .- 1558-2213. ; 32:16, s. 2862-2876
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Tidskriftsartikel (refereegranskat)abstract
- The channel capacity of a nonlinear, dispersive fiber-optic link is revisited. To this end, the popular Gaussian noise (GN) model is extended with a parameter to account for the finite memory of realistic fiber channels. This finite-memory model is harder to analyze mathematically but, in contrast to previous models, it is valid also for nonstationary or heavy-tailed input signals. For uncoded transmission and standard modulation formats, the new model gives the same results as the regular GN model when the memory of the channel is about ten symbols or more. These results confirm previous results that the GN model is accurate for uncoded transmission. However, when coding is considered, the results obtained using the finite-memory model are very different from those obtained by previous models, even when the channel memory is large. In particular, the peaky behavior of the channel capacity, which has been reported for numerous nonlinear channel models, appears to be an artifact of applying models derived for independent input in a coded (i.e., dependent) scenario. © 1983-2012 IEEE.
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| 3. |
- Agrell, Erik, 1965, et al.
(författare)
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First-order asymptotics of the BICM mutual information: Uniform vs. nonuniform distributions
- 2012
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Ingår i: Information Theory and Applications Workshop (ITA) 2012, San Diego, CA [Invited]. - 9781467314732 ; , s. 306 - 310
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Konferensbidrag (refereegranskat)abstract
- A linear, invertible transform is defined between two vectors or matrices as a tool for analyzing the bit-interleaved coded modulation (BICM) mutual information in the wideband regime. The transform coefficients depend on a set of real values, which can be interpreted as probabilities. The transform relates any BICM system with a nonuniform input distribution to another BICM system with a uniform distribution. Numerical evidence suggests that the two systems have the same first-order behavior, which would make possible to analyze nonuniform BICM systems based on known properties of uniform BICM systems.
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| 4. |
- Agrell, Erik, 1965, et al.
(författare)
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On optimal constellations for BICM at low SNR
- 2009
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Ingår i: Proceedings IEEE Information Theory Workshop ITW 2009, Taormina, Italy [Best Poster Award]. - 9781424449835 ; , s. 480-484
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Konferensbidrag (refereegranskat)abstract
- In this paper we study the problem of finding capacity-maximizing constellations in BICM for asymptotically low signal-to-noise ratios (SNRs). We base our analysis on the so-called Hadamard transform and on a linear approximation of the BICM capacity for asymptotically low SNRs. We fully characterize the set of constellations, input distributions, and binary labelings that achieve Shannon's limit E_b/N_0=-1.59 dB. For equiprobable input distributions, a constellation achieves this limit if and only if it is a linear projection of a hypercube.
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| 5. |
- Agrell, Erik, 1965, et al.
(författare)
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Optimal Alphabets and Binary Labelings for BICM at Low SNR
- 2011
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 57:10, s. 6650-6672
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Tidskriftsartikel (refereegranskat)abstract
- Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded binary code results in a higher capacity than the binary reflected gray code (BRGC) and the natural binary code (NBC). The 1 dB gap between the additive white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be almost completely removed if the input symbol distribution is properly selected. First-order asymptotics of the BICM capacity for arbitrary input alphabets and distributions, dimensions, mean, variance, and binary labeling are developed. These asymptotics are used to define first-order optimal (FOO) constellations for BICM, i.e. constellations that make BICM achieve the Shannon limit $-1.59 \tr{dB}$. It is shown that the $\Eb/N_0$ required for reliable transmission at asymptotically low rates in BICM can be as high as infinity, that for uniform input distributions and 8-PAM there are only 72 classes of binary labelings with a different first-order asymptotic behavior, and that this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general answer to the question of FOO constellations for BICM is also given: using the Hadamard transform, it is found that for uniform input distributions, a constellation for BICM is FOO if and only if it is a linear projection of a hypercube. A constellation based on PAM or quadrature amplitude modulation input alphabets is FOO if and only if they are labeled by the NBC; if the constellation is based on PSK input alphabets instead, it can never be FOO if the input alphabet has more than four points, regardless of the labeling.
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| 6. |
- Agrell, Erik, 1965, et al.
(författare)
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Signal Shaping for BICM at Low SNR
- 2013
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 59:4, s. 2396-2410
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Tidskriftsartikel (refereegranskat)abstract
- The generalized mutual information (GMI) of bit-interleaved coded modulation (BICM) systems, sometimes called the BICM capacity, is investigated at low signal-to-noise ratio (SNR). The combinations of input alphabet, input distribution, and binary labeling that achieve the Shannon limit are completely characterized. The main conclusion is that a BICM system with probabilistic shaping achieves the Shannon limit at low SNR if and only if it can be represented as a zero-mean linear projection of a hypercube. Hence, probabilistic shaping offers no extra degrees of freedom to optimize the low-SNR BICM-GMI, in addition to what is provided by geometrical shaping. The analytical conclusions are confirmed by numerical results, which also show that for a fixed input alphabet, probabilistic shaping can improve the BICM-GMI in the low and medium SNR range.
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| 7. |
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| 8. |
- Alvarado, Alex, 1982, et al.
(författare)
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Correcting Suboptimal Metrics in Iterative Decoders
- 2009
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Ingår i: IEEE International Conference on Communications. - 1550-3607. - 9781424434350
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Konferensbidrag (refereegranskat)abstract
- In this paper the issue of improving the performance of iterative decoders based on sub-optimal calculation of the messages exchanged during iterations (L-values) is addressed. It is well known in the literature that a simple---yet very effective---way to improve the performance of suboptimal iterative decoders is based on applying a scaling factor to the L-values. In this paper, starting with a theoretical model based on the so-called consistency condition of a random variable, we propose a methodology for correcting the L-values that relies only on the distribution of the soft information exchanged in the iterative process. This methodology gives a clear explanation of why the well-known linear scaling factor provides a very good performance. Additionally, the proposed methodology allows us to avoid the exhaustive search required otherwise. Numerical simulations show that for turbo codes the scaling factors found closely follow the optimum values, which translates to a close-to-optimal BER performance. Moreover, for LDPC codes, the proposed methodology produces a better BER performance compared with the known method in the literature.
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| 9. |
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| 10. |
- Alvarado, Alex, 1982, et al.
(författare)
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Distribution of L-values in Gray-mapped M^2-QAM: Closed-form Approximations and Applications
- 2009
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Ingår i: IEEE Transactions on Communications. - 1558-0857. ; 57:7, s. 2071-2079
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we develop closed form approximations for theprobability density function (PDF) of the reliability metrics (L-values) in bit-interleaved coded modulation (BICM). The expressions are valid for M^2-ary quadrature amplitude modulations (M^2-QAM) with Gray mapping when the metrics are calculated using the so-called max-log approximation. Based on the developed expressions, we also propose two simple Gaussian mixture approximations that are analytically tractable. We apply our developments to efficiently calculate the BICM channel capacity,and to develop bounds on the coded bit-error rate when aconvolutional code is used. The coded performance of an hybrid automatic repeat request (HARQ) based on constellation rearrangement is also evaluated.
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