V.R. Sidorenko, I. Martin, and B. Honary "On the rectangularity of nonlinear block codes," IEEE Trans. Inform. Theory, vol. 45, pp. 720--725, March 1999. Home/Search Document Not in Database Summary Related Articles Check |
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Ordered Binary Decision Diagrams and Minimal Trellises - Lafferty, Vardy (1998) (1 citation) (Correct)
....: x n ) be a Boolean function, and let x 1 OE Delta Delta Delta OEx n be an ordering of its variables. If the corresponding binary code C f is rectangular then the incoming edges of every nonterminal vertex in the OBDD for f(x 1 ; x n ) are labeled distinctly. Proof. It is known [69, 51, 75, 76] that the minimal proper trellis for a rectangular code is biproper. Thus if C f is a rectangular code with minimum distance d(C f ) 1, then the single terminal OBDD for f(x 1 ; x n ) is isomorphic to the minimal biproper trellis for C f , and hence all the incoming edges in the ....
....in this case. 0 1 x 1 x 2 x 3 x 3 Figure 5. A biproper OBDD for x 1 x 3 x 1 (x 2 x 3 x 2 x 3 ) Notice that whether the OBDD for f(x 1 ; x n ) is biproper depends not only on the function f(x 1 ; x n ) itself, but also on the ordering of its variables. Indeed, there exist codes [69] that are rectangular for some orderings of the time axis and non rectangular for other orderings. Finally, we observe that the sufficient condition for biproperness given in Proposition 2 is almost necessary as well. It is known [51] that a code is rectangular if and only if it admits a ....
V.R. Sidorenko, I. Martin, and B. Honary "On the rectangularity of nonlinear block codes," IEEE Trans. Inform. Theory, vol. 45, March 1999, to appear.
Ordered Binary Decision Diagrams - And Minimal Trellises (Correct)
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V.R. Sidorenko, I. Martin, and B. Honary "On the rectangularity of nonlinear block codes," IEEE Trans. Inform. Theory, vol. 45, pp. 720--725, March 1999.
On Some Linear Codes Over Z_2^s - Gupta (2000) (Correct)
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V. Sidorenko, I. Martin, and B. Honary. On the rectangularity of nonlinear block codes. IEEE Trans. Inform. Theory, 45(2):720--725, 1999.
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