| 1. |
- Bocharova, Irina, et al.
(författare)
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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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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 58:7, s. 4635-4644
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Tidskriftsartikel (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 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.
(författare)
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Searching for voltage graph-based LDPC tailbiting codes with large girth
- 2012
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 58:4, s. 2265-2279
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Tidskriftsartikel (refereegranskat)abstract
- The relation between parity-check matrices of quasi-cyclic (QC) low-density parity-check (LDPC) codes and biadjacency matrices of bipartite graphs supports searching for powerful LDPC block codes. Using the principle of tailbiting, compact representations of bipartite graphs based on convolutional codes can be found. Bounds on the girth and the minimum distance of LDPC block codes constructed in such a way are discussed. Algorithms for searching iteratively for LDPC block codes with large girth and for determining their minimum distance are presented. Constructions based on all-one matrices, Steiner Triple Systems, and QC block codes are introduced. Finally, new QC regular LDPC block codes with girth up to 24 are given.
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| 3. |
- Hug, Florian, et al.
(författare)
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A rate R=5/20 hypergraph-based woven convolutional code with free distance 120
- 2010
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 56:4, s. 1618-1623
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Tidskriftsartikel (refereegranskat)abstract
- A rate R=5/20 hypergraph-based woven convolu- tional code with overall constraint length 67 and constituent con- volutional codes is presented. It is based on a 3-partite, 3-uniform, 4-regular hypergraph and contains rate R=3/4 constituent convolutional codes with overall constraint length 5. Although the code construction is based on low-complexity codes, the free distance of this construction, computed with the BEAST algorithm, is dfree=120, which is remarkably large.
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