Abstract not found

Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed binary patterns. We show that the number of such sequences increases exponentially with their length and that the exponent, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We derive a new algorithm for determining the joint spectral radius of sets of nonnegative matrices and combine it with existing algorithms to determine the capacity of several sets of disallowed differences that arise in practice.

We establish that the feedback capacity of the trapdoor channel is the logarithm of the golden ratio and provide a simple communication scheme that achieves capacity. As part of the analysis, we formulate a class of dynamic programs that characterize capacities of unifilar finite-state channels. The trapdoor channel is an instance that admits a simple analytic solution.

A parallel constrained coding scheme is considered where p-blocks of raw data are encoded simultaneously into q tracks such that the contents of each track belong to a given constraint S. It is shown that as q increases, there are parallel block decodable encoders for S whose coding ratio, p/q, converges to the capacity of S. Examples are provided where parallel coding allows block decodable encoders, while conventional coding, at the same rate, does not. Parallel encoders are then applied as building blocks in the construction of block decodable encoders for certain families of two-dimensional constraints.

We derive lower bounds on the capacity of certain two-dimensional constraints by considering bounds on the entropy of measures induced by bit-stuffing encoders. A more detailed analysis of a previously proposed bit-stuffing encoder for (d � 1)-RLL constraints on the square lattice yields improved lower bounds on the capacity for all d 2. This encoding approach is extended to (d � 1)-RLL constraints on the hexagonal lattice, and a similar analysis yields lower bounds on capacity ford 2. For the hexagonal (1 � 1)-RLL constraint, the exact coding ratio of the bit-stuffing encoder is calculated and is shown to be within 0:5 % of the (known) capacity. Finally, alower bound is presented on the coding ratio of a bit-stuffing encoder for the constraint on the square lattice where each bit is equal to at least one of its four closest neighbors, thereby providing a lower bound on the capacity of this constraint.

The hard-square model, also known as the two-dimensional (1; 1)-RLL constraint, consists of all binary arrays in which the 1's are isolated both horizontally and vertically. Based on a certain probability measure defined on those arrays, an efficient variableto -fixed encoder scheme is presented that maps unconstrained binary words into arrays that satisfy the hard-square model. For sufficiently large arrays, the average rate of the encoder approaches a value which is only 0:1% below the capacity of the constraint. A second, fixed-rate encoder is presented whose rate for large arrays is within 1:2% of the capacity value. Keywords: Constrained codes; Enumerative coding; Hard-square model; Maxentropic probability measure; Permutation codes; Variable-to-fixed encoders; Twodimensional runlength-limited constraints. 1 Introduction In current digital optical and magnetic recording systems, such as disks and tapes, the data is written along tracks, thus visualized as a one-dimensional long ...

this article, we give an introduction to symbolic dynamics and then discuss some common themes in coding theory, automata theory and system theory. Although these subjects have grown up somewhat independently, there is a strong connection among them. In particular, they all study systems, representations of systems, and transformations from one system to another. For additional reading on the connections among these subjects, we refer the reader to the Mutilingual Dictionary, hereafter referred to as the Dictionary, which appears in this volume. For ease of reading, most of the terms that we use are defined within this article.

Abstract — A new variable-rate coding technique is presented for two-dimensional constraints. For certain constraints, such as the (0, 2)-RLL, (2, ∞)-RLL, and the “no isolated bits ” (n.i.b.) constraints, the technique is shown to improve on previouslypublished lower bounds on the capacity of the constraint. I.

Constructions are presented of finite-state encoders for certain (d; k)-RLL constraints with DC control. In particular, an example is provided for a rate 8 : 16 encoder for the (2; 10)-RLL constraint that requires no look-ahead in decoding, thus performing favorably compared to the EFMPlus code used in the DVD standard. Keywords: Runlength-limited coding, Optical recording, DC control, EFM code, EFMPlus code. Computer Science Department, Technion, Haifa 32000, Israel. E-mail: ronny@cs.technion.ac.il. This work was done in part while visiting Hewlett-Packard Laboratories, 1501 Page Mill Road, Palo Alto, CA, U.S.A., and in part at Hewlett-Packard Laboratories Israel, Haifa, Israel. 0 1 Introduction In optical and magnetic recording systems, the bit stream that is written into the device must satisfy certain constraints. The most common family of such constraints appears to be that of the (d; k)-runlength-limited (RLL) constraints, where the run of 0's between consecutive 1's in ...

Runlength-limited (d, k) constraints and codes are widely used in digital data recording and transmission applications. Generalizations of runlength constraints to two dimensions are of potential interest in page-oriented information storage systems. However, in contrast to the one-dimensional case, little is known about the information-theoretic properties of two-dimensional constraints or the design of practical, e#cient codes for them.