During the past five years, advances in the information-theoretic analysis of "one-dimensional (1D)" recording channels have clarified the limits on linear densities that can be achieved by
track-oriented magnetic and optical storage technologies. Channel architectures incorporating powerful codes, such as turbo codes and low-density parity-check codes, have been shown to achieve performance very close to the information-theoretic
As 1D track-oriented data storage technologies reach maturity, there is increasing interest in "two-dimensional (2D)" recording technologies, such as two-dimensional optical storage (TwoDOS) and holographic storage. This paper provides an overview of some recently developed techniques for determining analytical bounds and simulation-based
estimates for achievable densities of such 2D recording channels, as well as some recently proposed signal processing and coding methods that can move system performance closer to the information-theoretic limits.
Runlength-limited (d,k) constraints and codes are widely used in digital data recording and transmission applications. Generalizations of runlength constraints to two dimension 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, efficient codes for them. In this paper, we consider coding schemes that map unconstrained binary sequences into two- dimensional, runlength-limited (d, (infinity) ) constrained binary arrays, in which 1's are followed by at least d 0's in both the horizontal and vertical dimensions. We review the derivation of a lower bound on the capacity of two-dimensional (d, (infinity) ) constraints, for d greater than or equal to 1, obtained by bounding the average information rate of a variable-to-fixed rate encoding scheme, based upon a 'bit- stuffing' technique. For the special case of the two- dimensional (1, (infinity) ) constraint, upper and lower bounds on the capacity that are very close to being tight are known. For this constraint, we determine the exact average information rate of the bit-stuffing encoder, which turns out to be within 1% of the capacity of the constraint. We then present a fixed- rate, row-by-row encoding scheme for the two-dimensional (1, (infinity) ) constraint, somewhat akin to permutation coding, in which the rows of the code arrays represent 'typical' rows for the constraint. It is shown that, for sufficiently long rows, the rate of this encoding technique can almost achieve that of the variable-rate, bit-stuffing scheme.
Partial-response maximum-likelihood (PRML) methods are now being adopted in many digital magnetic recording systems. It is expected that as linear densities continue to increase, there will be a need to use 'extended' PRML techniques. In fact, commercial systems incorporating extended partial-response target channels, denoted EPRML and EEPRML, employing the EPR4 transfer polynomial h(D) equals 1 plus D minus D<SUP>2</SUP> minus D<SUP>3</SUP> and the EEPR4 transfer polynomial h(D) equals 1 plus 2D minus 2D<SUP>3</SUP> minus D<SUP>4</SUP>, respectively, have recently appeared. Among these systems, several apply the rate 2/3, (d,k) equals (1,7) runlength-limited code, originally designed for use with peak-detection, in combination with a detector trellis structure reflecting the d equals 1 constraint. In the EEPR4 case, the d equals 1 constraint is known to provide a coding gain of 2.2 dB, unnormalized for the rate loss, relative to the uncoded channel. In this paper, we describe a nested family of code constraints, properly containing the d equals 1 constraint, intended for use on the EEPR4 channel. These constraints are shown to have the same distance-enhancing properties as the d equals 1 constraint. They permit the design of practical codes for EEPR4 that offer the same coding gain as the (1,7)-coded system, but with higher achievable code rates. The paper concludes with the construction for such a code which, having rate 4/5, offers a 20% increase over the 1,7) code.