New techniques for bounding the channel capacity of read/write isolated memory

Abstract

Summary form only given. A serial binary (0,1) memory is read isolated if no two consecutive positions in the memory may both store 1's; it is write isolated if no two consecutive positions in the memory can be changed during rewriting. Such restrictions have arisen in the contexts of asymmetric error-correcting ternary codes and of rewritable optical discs etc. A read/write isolated memory is a binary, linearly ordered, rewritable storage medium that obeys both the read and write constraints. We introduce new compressed matrix techniques. The new contribution of this paper is to show that it is possible to take advantage of the recursive structures of the transfer matrices to (i) build other matrices of the same size whose eigenvalues yield provably better bounds or (ii) build smaller matrices whose largest eigenvalues are the same as those of the transfer matrices. Thus, it is possible to get the same bounds with less computation. We call these approaches compressed matrix techniques. While technique (ii) was specific to this problem technique (i) is applicable to many other two-dimensional constraint problems.