| 1. |
- Bocharova, Irina, et al.
(author)
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A Closed Form Expression for the Exact Bit Error Probability for Viterbi Decoding of Convolutional Codes
- 2012
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In: IEEE Transactions on Information Theory. - 0018-9448. ; 58:7, s. 4635-4644
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Journal article (peer-reviewed)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 formula was later extended to the rate R=1/2, memory m=2 (4-state) convolutional encoder with generator matrix G(D)=(1+D^2 1+D+D^2) by Lentmaier et al. In this paper, a different approach to derive the exact bit error probability is described. A general recurrent matrix equation, connecting the average information weight at the current and previous states of a trellis section of the Viterbi decoder, is derived and solved. The general solution of this matrix equation yields a closed form expression for the exact bit error probability. As special cases, the expressions obtained by Best et al. for the 2-state encoder and by Lentmaier et al. for a 4-state encoder are obtained. The closed form expression derived in this paper is evaluated for various realizations of encoders, including rate R=1/2 and R=2/3 encoders, of as many as 16 states. Moreover, it is shown that it is straightforward to extend the approach to communication over the quantized additive white Gaussian noise channel.
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| 2. |
- Bocharova, Irina, et al.
(author)
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A Greedy Search for Improved QC LDPC Codes with Good Girth Profile and Degree Distribution
- 2012
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In: IEEE International Symposium on Information Theory Proceedings (ISIT), 2012. - 9781467325806 ; , s. 3083-3087
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Conference paper (peer-reviewed)abstract
- Search algorithms for regular and irregular quasi-cyclic LDPC block codes with both good girth profile and good degree distribution are presented. New QC LDPC block codes of various code rates are obtained and their bit error rate performance is compared with that of the corresponding LDPC block codes defined in the IEEE 802.16 WiMAX standard of the same block length and code rate.
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| 3. |
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| 4. |
- Bocharova, Irina, et al.
(author)
-
Another look at the exact bit error probability for Viterbi decoding of convolutional codes
- 2011
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Conference paper (peer-reviewed)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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| 5. |
- Bocharova, Irina, et al.
(author)
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Combinatorial Optimization for Improving QC LDPC codes performance
- 2013
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In: IEEE International Symposium on Information Theory (ISIT). - 2157-8095 .- 2157-8117. ; , s. 2651-2655
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Conference paper (peer-reviewed)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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| 6. |
- Bocharova, Irina, et al.
(author)
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Double-Hamming based QC LDPC codes with large minimum distance
- 2011
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In: [Host publication title missing].
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Conference paper (peer-reviewed)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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| 7. |
- Bocharova, Irina, et al.
(author)
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Dual convolutional codes and the MacWilliams identities
- 2012
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In: Problems of Information Transmission. - 0032-9460. ; 48:1, s. 21-30
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Journal article (peer-reviewed)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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| 8. |
- Bocharova, Irina, et al.
(author)
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High-Rate QC LDPC Codes of Short and Moderate Length with Good Girth Profile
- 2012
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In: 7th International Symposium on Turbo Codes and Iterative Information Processing (ISTC), 2012. - 9781457721144 ; , s. 150-154
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Conference paper (peer-reviewed)abstract
- Irregular QC LDPC codes with parity-check matrices having different degree distributions are studied. A new algorithm for finding regular and irregular QC LDPC codes with a good girth profile as well as a good sliding-window girth is presented. As examples, simulation results for QC LDPC codes with good girth profile, rate R=4/5, and lengths about 1000, 2000, and 4000, constructed from base matrices with proper degree distributions are given. Their simulated BER and FER performances for belief propagation decoding are compared with the best previously known irregular QC LDPC codes of the same rate and length. It is shown that the constructed codes outperform the best previously known codes of same rate and lengths.
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