A binary sequence satisfies a one-dimensional (d,k) run length constraint if every run of zeros has length at least d and at most k. A two-dimensional binary pattern is (d/sub 1/,k/sub 1/,d/sub 2/,k/sub 2/)-constrained if it satisfies the one-dimensional (d/sub 1/,k/sub 1/) run length constraint horizontally and the one-dimensional (d/sub 2/,k/sub 2/) run length constraint vertically. For given d/sub 1/, k/sub 1/, d/sub 2/, and k/sub 2/, the asymmetric two-dimensional capacity is defined as C/sub d1,k1,d2,k2/=lim/sub m,n/spl rarr//spl infin// (1/(mn)) log/sub 2/ N/sub m,n//sup (d1,k1,d2,k2)/ where N/sub m,n//sup (d1,k1,d2,k2)/ denotes the number of (d/sub 1/,k/sub 1/,d/sub 2/,k/sub 2/)-constrained m/spl times binary patterns. We determine whether the capacity is positive or is zero, for many choices of (d/sub 1/,k/sub 1/,d/sub 2/,k/sub 2/).
展开▼
机译：如果每个零位游程的长度至少为d且最大为k，则二进制序列满足一维（d，k）游程长度约束。如果二维二进制模式满足一维（d / sub 1 /，k / sub 2 /，k / sub 2 /，k / sub 2 /），则约束该二维二进制模式。 sub 1 /）游程长度约束水平，一维（d / sub 2 /，k / sub 2 /）游程长度约束垂直。对于给定的d / sub 1 /，k / sub 1 /，d / sub 2 /和k / sub 2 /，不对称二维电容定义为C / sub d1，k1，d2，k2 / = lim / sub m，n / spl rarr // spl infin //（1 /（mn））log / sub 2 / N / sub m，n // sup（d1，k1，d2，k2）/其中N / sub m， n // sup（d1，k1，d2，k2）/表示受（d / sub 1 /，k / sub 1 /，d / sub 2 /，k / sub 2 /）约束的m / spl次/ n个二进制模式。对于（d / sub 1 /，k / sub 1 /，d / sub 2 /，k / sub 2 /）的许多选择，我们确定容量为正还是为零。
展开▼
