Skip-Sliding Window Codes

Constrained coding is used widely in digital communication and storage systems. In this paper, we study a generalized sliding window constraint called the skip-sliding window. A skip-sliding window (SSW) code is defined in terms of the length $L$ of a sliding window, skip length $J$, and cost constraint $E$ in each sliding window. Each valid codeword of length $L + kJ$ is determined by $k+1$ windows of length $L$ where window $i$ starts at $(iJ + 1)$th symbol for all non-negative integers $i$ such that $i \leq k$; and the cost constraint $E$ in each window must be satisfied. In this work, two methods are given to enumerate the size of SSW codes and further refinements are made to reduce the enumeration complexity. Using the proposed enumeration methods, the noiseless capacity of binary SSW codes is determined and observations such as greater capacity than other classes of codes are made. Moreover, some noisy capacity bounds are given. SSW coding constraints arise in various applications including simultaneous energy and information transfer.Comment: 28 pages, 11 figure

M-ary run length limited coding

This thesis consists of two parts: 1) a result of the rationality of channel capacity for the M -ary (d, k) constraint, and 2) a software package which has been designed to aid in the development of efficient, high density channel encoders for M -ary (d, k) constrained recording code. It has been written for the platforms of IBM PC or PC compatible and Sun Workstations. The designed software in this thesis involves three steps. The first step is to calculate the capacity of a RLL code after the user has chosen (M,d,k) . The channel capacity specifies the maximum ratio of information ( p ) bits/codeword ( q ) bits achievable in implementing these codes and gives options of code choice for any specific task. The second step is to find a code efficiency (eta) = R/C by choosing p and q , and display the state transition matrix of finite state transition diagram and finite state transition diagram of the code. The last step is to aid the user in the generation of a code, by using state splitting algorithm of R. Adler, D. Coppersmith and M. Hassner [10]

Time-Space Constrained Codes for Phase-Change Memories

Phase-change memory (PCM) is a promising non-volatile solid-state memory technology. A PCM cell stores data by using its amorphous and crystalline states. The cell changes between these two states using high temperature. However, since the cells are sensitive to high temperature, it is important, when programming cells, to balance the heat both in time and space. In this paper, we study the time-space constraint for PCM, which was originally proposed by Jiang et al. A code is called an \emph{$(\alpha,\beta,p)$-constrained code} if for any $\alpha$ consecutive rewrites and for any segment of $\beta$ contiguous cells, the total rewrite cost of the $\beta$ cells over those $\alpha$ rewrites is at most $p$. Here, the cells are binary and the rewrite cost is defined to be the Hamming distance between the current and next memory states. First, we show a general upper bound on the achievable rate of these codes which extends the results of Jiang et al. Then, we generalize their construction for $(\alpha\geq 1, \beta=1,p=1)$-constrained codes and show another construction for $(\alpha = 1, \beta\geq 1,p\geq1)$-constrained codes. Finally, we show that these two constructions can be used to construct codes for all values of $\alpha$, $\beta$, and $p$