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Matrix representations of trellises and enumerating trellis pseudocodewords
- Source :
- Allerton
- Publication Year :
- 2011
- Publisher :
- IEEE, 2011.
-
Abstract
- Tail-biting trellises and their pseudocodewords are very important for modern decoding techniques like iterative decoding. We introduce a useful matrix representation of trellises, give its fundamental properties, and use it to enumerate and describe the distribution of trellis pseudocodewords. We give several examples, a couple of which lead to important open problems. Next, we prove that the pseudocodeword weight enumerator introduced in [2] always satisfies a recurrence equation, and, for certain trellises including the Golay trellis given in [3], that it is invariant under generalized MacWilliams transformations, allowing invariant theory to be used for computing it. Computation for the Golay trellis shows then that pseudocodewords of period at most 4 must have AWGN pseudoweight at least 8.
Details
- Database :
- OpenAIRE
- Journal :
- 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- Accession number :
- edsair.doi...........7eec89d17f0c19f63438be66bcb31be4