| 11. |
- Bocharova, Irina, et al.
(författare)
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Another look at the exact bit error probability for Viterbi decoding of convolutional codes
- 2011
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Konferensbidrag (refereegranskat)abstract
- In 1995, Best et al. published a formula for the exact bit error probability for Viterbi decoding of the rate R=1/2, memory m=1 (2-state) convolutional encoder with generator matrix G(D)=(1 1+D) when used to communicate over the binary symmetric channel. Their method was later extended to the rate R=1/2, memory m=2 (4-state) generator matrix G(D)=(1+D^2 1+D+D^2) by Lentmaier et al. In this paper, we shall use a different approach to derive the exact bit error probability. We derive and solve a general matrix recurrent equation connecting the average information weights at the current and previous steps of the Viterbi decoding. A closed form expression for the exact bit error probability is given. Our general solution yields the expressions for the exact bit error probability obtained by Best et al. (m=1) and Lentmaier et al. (m=2) as special cases. The exact bit error probability for the binary symmetric channel is determined for various 8 and 16 states encoders including both polynomial and rational generator matrices for rates R=1/2 and R=2/3. Finally, the exact bit error probability is calculated for communication over the quantized additive white Gaussian noise channel.
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| 12. |
- Bocharova, Irina, et al.
(författare)
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Asymptotic performance of woven graph codes
- 2008
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Ingår i: [Host publication title missing]. - 9781424422562 ; , s. 1025-1029
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Konferensbidrag (refereegranskat)abstract
- Constructions of woven graph codes based on constituent block and convolutional codes are studied. It is shown that within the random ensemble of such codes based on s-partite, s-uniform hypergraphs, where s depends only on the code rate, there exist codes satisying the Varshamov-Gilbert (VG) and the Costello lower bound on the minimum distance and the free distance, respectively.
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| 13. |
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| 14. |
- Bocharova, Irina, et al.
(författare)
-
BEAST decoding - asymptotic complexity
- 2005
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Ingår i: 2005 IEEE Information Theory Workshop. - 0780394801
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Konferensbidrag (refereegranskat)abstract
- BEAST is a bidirectional efficient algorithm for searching trees that performs soft-decision maximum-likelihood (ML) decoding of block codes. The decoding complexity of BEAST is significantly reduced compared to the Viterbi algorithm. An analysis of the asymptotic BEAST decoding complexity verifies BEAST's high efficiency compared to other algorithms. The best of the obtained asymptotic upper bounds on the BEAST decoding complexity is better than previously known bounds for ML decoding in a wide range of code rates.
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| 15. |
- Bocharova, Irina, et al.
(författare)
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BEAST decoding for block codes
- 2004
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Ingår i: ITG-Fachbericht. - : Wiley. - 0932-6022. ; 15:4, s. 297-305
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Konferensbidrag (refereegranskat)abstract
- BEAST is a Bidirectional Efficient Algorithm for Searching code Trees. In this paper, it is used for decoding block codes over the additive white Gaussian noise (AWGN) channel. If no constraints are imposed on the decoding complexity (in terms of the number of visited nodes during the search), BEAST performs maximum-likelihood (ML) decoding. At the cost of a negligible performance degradation, BEAST can be constrained to perform almost-ML decoding with significantly reduced complexity. The benchmark for the complexity assessment is the number of nodes visited by the Viterbi algorithm operating on the minimal trellis of the code. The decoding complexity depends on the trellis structure of a given code, which is illustrated by three different forms of the generator matrix for the (24, 12, 8) Golay code. Simulation results are also presented for two other codes
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| 16. |
- 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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| 17. |
- Bocharova, Irina, et al.
(författare)
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Combinatorial Optimization for Improving QC LDPC codes performance
- 2013
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Ingår i: IEEE International Symposium on Information Theory (ISIT). - 2157-8095 .- 2157-8117. ; , s. 2651-2655
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Konferensbidrag (refereegranskat)abstract
- Techniques for searching for good quasi-cyclic (QC) LDPC block codes of short and moderate lengths which are suitable for practical purposes are studied. To facilitate implementations only codes whose parity-check matrices having bidiagonal structure of their submatrices and consequently having low encoding complexity are considered. The problem of finding QC LDPC codes with the near-optimum frame or bit error rate performance is split into two independent steps: searching for the near-optimum column degree distribution of the parity-check matrix together with the best base matrix for this degree distribution and searching for the near-optimum labeling of the chosen base matrix. Sets of parameters and criteria for both steps are introduced and discussed. They allow further reduction of the search complexity without significant loss of the search optimality. New QC LDPC block codes of various code rates are obtained and their BER and FER performances are compared with those of the LDPC block codes as well as the turbo codes defined in the IEEE 802.16 WiMAX standard.
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| 18. |
- Bocharova, Irina, et al.
(författare)
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Convolutional codes with large slopes yield better tailbiting codes
- 2002
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Ingår i: IEEE International Symposium on Information Theory, 2002. Proceedings.. - 0780375017 ; , s. 258-258
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Konferensbidrag (refereegranskat)abstract
- Upper bounds on the slope of the active distances for convolutional codes are given. Convolutional codes with large slopes are used to obtain tables of new tailbiting block codes.
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| 19. |
- Bocharova, Irina, et al.
(författare)
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Double-Hamming based QC LDPC codes with large minimum distance
- 2011
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Ingår i: [Host publication title missing].
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Konferensbidrag (refereegranskat)abstract
- A new method using Hamming codes to construct base matrices of (J, K)-regular LDPC convolutional codes with large free distance is presented. By proper labeling the corresponding base matrices and tailbiting these parent convolutional codes to given lengths, a large set of quasi-cyclic (QC) (J, K)-regular LDPC block codes with large minimum distance is obtained. The corresponding Tanner graphs have girth up to 14. This new construction is compared with two previously known constructions of QC (J, K)-regular LDPC block codes with large minimum distance exceeding (J+1)!. Applying all three constructions, new QC (J, K)-regular block LDPC codes with J=3 or 4, shorter codeword lengths and/or better distance properties than those of previously known codes are presented.
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| 20. |
- Bocharova, Irina, et al.
(författare)
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Dual convolutional codes and the MacWilliams identities
- 2012
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Ingår i: Problems of Information Transmission. - 0032-9460. ; 48:1, s. 21-30
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Tidskriftsartikel (refereegranskat)abstract
- A recursion for sequences of spectra of truncated as well as tailbitten convolutional codes and their duals is derived. The order of this recursion is shown to be less than or equal to the rank of the weight adjacency matrix (WAM) for the minimal encoder of the convolutional code. It is sufficient to know finitely many spectra of these terminated convolutional codes in order to obtain an infinitely long sequence of spectra of their duals.
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