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Problemy Peredachi Informatsii, 1997, Volume 33, Issue 1, Pages 87–93
(Mi ppi362)
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This article is cited in 12 scientific papers (total in 12 papers)
Coding Theory
The Euler Characteristic of the Minimal Code Trellis is Maximum
V. R. Sidorenko
Abstract:
A class of separable block codes is defined. The class includes group and linear codes. A code trellis is called the minimal trellis if it has the minimum number of vertices $|V|$| (the order of code symbols is fixed). We show that the minimal trellis of a separable code minimizes the edge count $|E|$ and maximizes the Euler characteristic $|V|-|E|$. Thus, the Viterbi decoding complexity of a separable code is minimum when it is implemented on the minimal code trellis, since the Viterbi decoding algorithm requires $|E|$ additions and $|E|-|V|+1$ comparisons.
Received: 19.04.1996
Citation:
V. R. Sidorenko, “The Euler Characteristic of the Minimal Code Trellis is Maximum”, Probl. Peredachi Inf., 33:1 (1997), 87–93; Problems Inform. Transmission, 33:1 (1997), 72–77
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https://www.mathnet.ru/eng/ppi362 https://www.mathnet.ru/eng/ppi/v33/i1/p87
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