| 1. |
- Agrell, Erik, 1965, et al.
(författare)
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Gray coding for multilevel constellations in Gaussian noise
- 2007
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 53:1, s. 224-235
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Tidskriftsartikel (refereegranskat)abstract
- The problem of finding the optimal labeling (bit-to-symbol mapping) of multilevel coherent phase shift keying (PSK), pulse amplitude modulation (PAM), and quadrature amplitude modulation (QAM) constellations with respect to minimizing the bit-error probability (BEP) over a Gaussian channel is addressed. We show that using the binary reflected Gray code (BRGC) to label the signal constellation results in the lowest possible BEP for high enough signal energy-to-noise ratios and analyze what is "high enough"in this sense. It turns out that the BRGC is optimal for PSK and PAM systems whenever the target BEP is at most a few percent, which covers most systems of practical interest. New and simple closed-form expressions are presented for the BEP of PSK, PAM, and QAM using the BRGC. © 2007 IEEE.
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| 2. |
- Anderson, John B, et al.
(författare)
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On the BCJR algorithm for rate-distortion source coding
- 2007
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 53:9, s. 3201-3207
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Tidskriftsartikel (refereegranskat)abstract
- The BCJR algorithm is an important channel decoding method. We extend it to trellis rate-distortion data compression. Beginning from source coding principles, the derivation of the algorithm avoids channel coding or soft output ideas. The encoder does not use entropy coding; equiprobable reproducer letters are emphasized since these maximize entropy. The BCJR method is demonstrated by tests of a tailbiting variant. It performs much better than the ordinary Viterbi algorithm for short and medium blocks. However, the improvement stems from tailbiting; the role of the BCJR is to achieve tailbiting in a relatively simple way. Some issues that arise with tailbiting are explored. It is shown that there is an optimal trellis state size for each block length.
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| 3. |
- Asraf, Daniel, et al.
(författare)
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Detection of Multiple Transient Signals with Unknown Arrival Times
- 2005
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 51:5, s. 1856-1860
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Tidskriftsartikel (refereegranskat)abstract
- The problem of optimal detection of signal transients with unknown arrival times contaminated by additive Gaussian noise is considered. The transients are assumed to be time continuous and belong to a parameterized family with the uncertainty about the parameters described by means of an a priori distribution. Under the assumption of a negligible probability that the independent transient observations overlap in time, a likelihood ratio is derived for the problem of detecting an unknown number of transients from the family, each transient with unknown arrival time. The uncertainty about the arrival times is assumed to be equal for all transients and is also described by means of a distribution. Numerical simulations of the performance of detecting a particular transient signal family are presented in the form of receiver operating characteristics (ROCs) for both the optimal detector and the classical generalized likelihood ratio test (GLRT). The results show that the optimal detector yields noticeable performance improvements over the GLRT. Moreover, the results show that the optimal detector may still outperform the GLRT when the true and modeled uncertainties about arrival times no longer agree.
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| 4. |
- Aulin, Tor, 1948
(författare)
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Comment on “Improved Analysis of List Decoding and Its Application to Convolutional Codes and Turbo Codes”
- 2009
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 55:8, s. 3892-
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Tidskriftsartikel (refereegranskat)abstract
- In a recent paper (Bai et al, IEEE Trans. Inf. Theory, 2007) an improved analysis concerning the analysis of List Decoding was presented. The event that the correct codeword is excluded from the list is central. For the additive white Gaussian noise (AWGN) channel an important quantity is the in (Bai et al, IEEE Trans. Inf. Theory, 2007) called effective Euclidean distance. This was earlier considered in (Aulin, IEEE Trans. Commun., 1999) under the name Vector Euclidean Distance, where also a simple mathematical expression for this quantity was easily derived for any list size. In (Bai et al, IEEE Trans. Inf. Theory, 2007), a geometrical analysis gives this when the list size is 1, 2 or 3.
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| 5. |
- Bocharova, Irina, et al.
(författare)
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An improved bound on the list error probability and list distance properties
- 2008
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 54:1, s. 13-32
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Tidskriftsartikel (refereegranskat)abstract
- List decoding of binary block codes for the additive white Gaussian noise channel is considered. The output of a list decoder is a list of the $L$ most likely codewords, that is, the L signal points closest to the received signal in the Euclidean-metric sense. A decoding error occurs when the transmitted codeword is not on this list. It is shown that the list error probability is fully described by the so-called list configuration matrix, which is the Gram matrix obtained from the signal vectors forming the list. The worst-case list configuration matrix determines the minimum list distance of the code, which is a generalization of the minimum distance to the case of list decoding. Some properties of the list configuration matrix are studied and their connections to the list distance are established. These results are further exploited to obtain a new upper bound on the list error probability, which is tighter than the previously known bounds. This bound is derived by combining the techniques for obtaining the tangential union bound with an improved bound on the error probability for a given list. The results are illustrated by examples.
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| 6. |
- Bocharova, Irina, et al.
(författare)
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BEAST decoding of block codes obtained via convolutional codes
- 2005
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 51:5, s. 1880-1891
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Tidskriftsartikel (refereegranskat)abstract
- BEAST is a bidirectional efficient algorithm for searching trees. In this correspondence, BEAST is extended to maximum-likelihood (ML) decoding of block codes obtained via convolutional codes. First it is shown by simulations that the decoding complexity of BEAST is significantly less than that of the Viterbi algorithm. Then asymptotic upper bounds on the BEAST decoding complexity for three important ensembles of codes are derived. They verify BEAST's high efficiency compared to other algorithms. For high rates, the new asymptotic bound for the best ensemble is in fact better than previously known bounds.
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| 7. |
- Bocharova, Irina, et al.
(författare)
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Trellis complexity of short linear codes
- 2007
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 53:1, s. 361-368
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Tidskriftsartikel (refereegranskat)abstract
- An extended table of Shuurman's bounds on the state complexity of short binary linear codes is presented. Some new lower and upper bounds are obtained. Most of the newly found codes are based on the so-called double zero-tail termination (DZT) construction
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| 8. |
- 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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| 9. |
- 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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| 10. |
- 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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