| 1. |
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| 2. |
- 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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| 3. |
- Brännström, Fredrik, 1974, et al.
(författare)
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Classification of Unique Mappings for 8PSK Based on Bit-Wise Distance Spectra
- 2009
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 55:3, s. 1131-1145
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Tidskriftsartikel (refereegranskat)abstract
- The performance of bit-interleaved coded modulation (BICM) with (or without) iterative decoding (ID) is significantly influenced by the mapping of bits to the symbol constellation. Our main objective in this paper is to develop a systematic design approach for BICM-ID schemes, ensuring the best possible performance with iterative decoding. Although useful mappings for BICM-ID have been found based on various search strategies, no attempt has been made to systematically enumerate and classify all unique mappers for a given constellation. As the basis for a systematic enumeration and classification, we define the average bit-wise distance spectrum for a mapping from bits to symbols. Different bit-wise distance spectra are derived assuming no prior information or full prior information, respectively. The bit-wise distance spectra determine corresponding bit-wise error probability and bit-wise mutual information. The latter allows us to use the classification of mappings with unique bit-wise distance spectra to also classify mappings with unique extremal points in the corresponding extrinsic information transfer (EXIT) curves. As an example of our approach, we classify 8PSK mappings into 86 classes of unique mappings according to bit-wise distance spectra. The classification can be used to significantly reduce the complexity of the search for suitable mappers for BICM-ID. For 8PSK and a given encoder, only 86 different mappings need to be, investigated. As examples of the systematic design approach, the best 8PSK mappings for minimizing the convergence threshold are found for concatenation with the rate 1/2 (5, 7)(8) and (133, 171)(8) convolutional codes, and the rate 1/2 UMTS turbo code with identical constituent convolutional codes (15/13)(8).
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| 4. |
- Brännström, Fredrik, 1974, et al.
(författare)
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Convergence analysis and optimal scheduling for multiple concatenated codes
- 2005
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 51:9, s. 3354-3364
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Tidskriftsartikel (refereegranskat)abstract
- An interesting practical consideration for decoding of serial or parallel concatenated codes with more than two components is the determination of the lowest complexity component decoder schedule which results in convergence. This correspondence presents an algorithm that finds such an optimal decoder schedule. A technique is also given for combining and projecting a series of three-dimensional extrinsic information transfer (EXIT) functions onto a single two-dimensional EXIT chart. This is a useful technique for visualizing the convergence threshold for multiple concatenated codes and provides a design tool for concatenated codes with more than two components.
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| 5. |
- Brännström, Fredrik, 1974, et al.
(författare)
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Optimal Puncturing Ratios and Energy Allocation for Multiple Parallel Concatenated Codes
- 2009
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 55:5, s. 2062-2077
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Tidskriftsartikel (refereegranskat)abstract
- We propose a systematic design framework for optimal, low-complexity punctured multiple parallel concatenated codes (MPCCs), based on minimizing the convergence threshold using extrinsic information transfer (EXIT) charts. As the convergence threshold is related to the area between the two EXIT curves, the corresponding optimization problem is equivalent to a curve-fitting problem. The EXIT curves are determined by the respective EXIT functions of the constituents, which can be conveniently shaped through the use of random puncturing and unequal energy allocations across parallel coding streams. The design task is therefore to find the optimal combination of constituents, puncturing ratios, and energy allocation for matching the EXIT curves. A search over all rate-one convolutional codes of memory length four or less is performed, identifying 98 classes of codes with unique EXIT functions out of a total of 310 codes. Low-complexity MPCCs with up to four constituents are found, where the convergence thresholds are observed to be within 0.1 dB or less of the fundamental minimum signal-to-noise ratio (SNR) corresponding to the binary phase-shift keying (BPSK) capacity for code rates 1/3
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| 6. |
- Häger, Christian, 1986, et al.
(författare)
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Density Evolution for Deterministic Generalized Product Codes on the Binary Erasure Channel at High Rates
- 2017
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 63:7, s. 4357-4378
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Tidskriftsartikel (refereegranskat)abstract
- Generalized product codes (GPCs) are extensions of product codes (PCs), where code symbols are protected by two component codes but not necessarily arranged in a rectangular array. We consider a deterministic construction of GPCs (as opposed to randomized code ensembles) and analyze the asymptotic performance over the binary erasure channel under iterative decoding. Our code construction encompasses several classes of GPCs previously proposed in the literature, such as irregular PCs, blockwise braided codes, and staircase codes. It is assumed that the component codes can correct a fixed number of erasures and that the length of each component code tends to infinity. We show that this setup is equivalent to studying the behavior of a peeling algorithm applied to a sparse inhomogeneous random graph. Using a convergence result for these graphs, we derive the density evolution equations that characterize the asymptotic decoding performance. As an application, we discuss the design of irregular GPCs, employing a mixture of component codes with different erasure-correcting capabilities.
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| 7. |
- Ivanov, Mikhail, 1986, et al.
(författare)
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On the Asymptotic Performance of Bit-Wise Decoders for Coded Modulation
- 2014
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 60:5, s. 2796-2804
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Tidskriftsartikel (refereegranskat)abstract
- Two decoder structures for coded modulation over the Gaussian channel are studied: the maximum likelihood symbol-wise decoder, and the (suboptimal) bit-wise decoder based on the bit-interleaved coded modulation paradigm. We consider a 16-ary quadrature amplitude constellation labeled with a Gray labeling. It is shown that the asymptotic loss in terms of pairwise error probability, for any two codewords caused by the bit-wise decoder, is bounded by 1.25 dB. The analysis also shows that the asymptotic loss is zero for a wide range of linear codes, including all rate-1/2 convolutional codes.
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| 8. |
- Ivanov, Mikhail, 1986, et al.
(författare)
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On the Information Loss of the Max-Log Approximation in BICM Systems
- 2016
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 62:6, s. 3011 - 3025
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Tidskriftsartikel (refereegranskat)abstract
- We present a comprehensive study of the information rate loss of the max-log approximation for M-ary pulse-amplitude modulation (PAM) in a bit-interleaved coded modulation (BICM) system. It is widely assumed that the calculation of L-values using the max-log approximation leads to an information loss. We prove that this assumption is correct for all M-PAM constellations and labelings with the exception of a symmetric 4-PAM constellation labeled with a Gray code. We also show that for max-log L-values, the BICM generalized mutual information (GMI), which is an achievable rate for a standard BICM decoder, is too pessimistic. In particular, it is proved that the so-called harmonized GMI, which can be seen as the sum of bit-level GMIs, is achievable without any modifications to the decoder. We then study how bit-level channel symmetrization and mixing affect the MI and the GMI for max-log L-values. Our results show that these operations, which are often used when analyzing BICM systems, preserve the GMI. However, this is not necessarily the case when the MI is considered. Necessary and sufficient conditions under which these operations preserve the MI are provided.
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| 9. |
- Sokolovskii, Roman, 1993, et al.
(författare)
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Finite-Length Scaling of SC-LDPC Codes With a Limited Number of Decoding Iterations
- 2023
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 69:8, s. 4869-4888
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Tidskriftsartikel (refereegranskat)abstract
- We propose four finite-length scaling laws to predict the frame error rate (FER) performance of spatially-coupled low-density parity-check codes under full belief propagation (BP) decoding with a limit on the number of decoding iterations and a scaling law for sliding window decoding, also with limited iterations. The laws for full BP decoding provide a choice between accuracy and computational complexity; a good balance between them is achieved by the law that models the number of decoded bits after a certain number of BP iterations by a time-integrated Ornstein-Uhlenbeck process. This framework is developed further to model sliding window decoding as a race between the integrated Ornstein-Uhlenbeck process and an absorbing barrier that corresponds to the left boundary of the sliding window. The proposed scaling laws yield accurate FER predictions.
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