A binary sequence satisfies a one-dimensional\$(d_1, k_1, d_2, k_2)\$runlength constraint if every run of zeros has length at least\$d_1\$and at most\$k_1\$and every run of ones has length at least\$d_2\$and at most\$k_2\$. A two-dimensional binary array is\$(d_1, k_1, d_2, k_2; d_3, k_3, d_4, k_4)\$-constrained if it satisfies the one-dimensional\$(d_1, k_1, d_2, k_2)\$runlength constraint horizontally and the one-dimensional\$(d_3, k_3, d_4, k_4)\$runlength constraint vertically. For given\$d_1, k_1, d_2, k_2, d_3, k_3, d_4, k_4\$, the two-dimensional capacity is defined as \$\$displaylines C(d_1, k_1, d_2, k_2; d_3, k_3, d_4, k_4) hfillcr hfill=, lim_m,n rightarrow infty log_2 N(m, n ,vert, d_1, k_1, d_2, k_2; d_3, k_3, d_4, k_4)over mn \$\$ where \$\$N(m, n ,vert, d_1, k_1, d_2, k_2; d_3, k_3, d_4, k_4)\$\$ denotes the number of\$m times n\$binary arrays that are\$(d_1, k_1, d_2, k_2; d_3, k_3, d_4, k_4)\$-constrained. Such constrained systems may have applications in digital storage applications. We consider the question for which values of\$d_i\$and\$k_i\$is the capacity\$C(d_1, k_1, d_2, k_2; d_3, k_3, d_4, k_4)\$positive and for which values is the capacity zero. The question is answered for many choices of the\$d_i\$and the\$k_i\$.

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Information Theory, IEEE Transactions on  (Volume:51 ,  Issue: 9 )

Sept. 2005