| 1. |
- 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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| 2. |
- 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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| 3. |
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| 4. |
- Bocharova, Irina, et al.
(författare)
-
On the exact bit error probability for Viterbi decoding of convolutional codes
- 2011
-
Konferensbidrag (refereegranskat)abstract
- Forty years ago, Viterbi published upper bounds on both the first error event (burst error) and bit error probabilities for Viterbi decoding of convolutional codes. These bounds were derived using a signal flow chart technique for convolutional encoders. 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 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 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.
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| 5. |
- Bocharova, Irina, et al.
(författare)
-
Some Voltage Graph-Based LDPC Tailbiting Codes with Large Girth
- 2011
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Ingår i: [Host publication title missing].
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Konferensbidrag (refereegranskat)abstract
- The relation between the parity-check matrices of quasi-cyclic (QC) low-density parity-check (LDPC) codes and the biadjacency matrices of bipartite graphs supports searching for powerful LDPC block codes. Algorithms for searching iteratively for LDPC block codes with large girth are presented and constructions based on Steiner Triple Systems and short QC block codes are introduced, leading to new QC regular LDPC block codes with girth up to 24.
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| 6. |
- Bocharova, Irina, et al.
(författare)
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Woven convolutional graph codes with large free distances
- 2011
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Ingår i: Problems of Information Transmission. - 0032-9460. ; 47:1, s. 1-14
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Tidskriftsartikel (refereegranskat)abstract
- Constructions of woven graph codes based on constituent convolutional codes are studied and examples of woven convolutional graph codes are presented. The existence of codes, satisfying the Costello lower bound on the free distance, within the random ensemble of woven graph codes based on s-partite, s-uniform hypergraphs, where s depends only on the code rate, is shown. Simulation results for Viterbi decoding of woven graph codes are presented and discussed.
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| 7. |
- Johnsson, Daniel, et al.
(författare)
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Searching for new convolutional codes using the cell broadband engine architecture
- 2011
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Ingår i: IEEE Communications Letters. - 1089-7798. ; 15:5, s. 560-562
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Tidskriftsartikel (refereegranskat)abstract
- The Bidirectional Efficient Algorithm for Searching code Trees (BEAST), which is an algorithm to efficiently determine the free distance and spectral components of convolutional encoders, is implemented for the Cell Broadband Engine Architecture, efficiently utilizing the underlying hardware. Exhaustive and random searches are carried out, presenting new rate R=1/2 convolutional encoding matrices with memory m=26 - 29 and larger free distances and/or fewer spectral components than previously known encoding matrices of same rate and complexity. The main result of this paper consists in determining the previously unknown optimum free distance convolutional code with memory m=26.
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