Block codes for a class of constrained noiseless channels

Abstract-We examine the well-known problem of determining the capacity of multidimensional run-length-limited constrained systems. By recasting the problem, which is essentially a combinatorial counting problem, into a probabilistic setting, we are able to derive new lower and upper bounds on the capacity of (0; k)-RLL systems. These bounds are better than all previously-known analytical bounds for k 2, and are tight asymptotically. Thus, we settle the open question: what is the rate at which the capacity of (0; k)-RLL systems converges to 1 as k ! 1? We also provide the first nontrivial upper bound on the capacity of general (d; k)-RLL systems.

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“…This constraint was first narrowly defined by Kautz [13], and later generalized to its current -RLL form by Tang and Bahl [29].…”

Section: Introductionmentioning

confidence: 99%

New Bounds on the Capacity of Multidimensional Run-Length Constraints

Schwartz

Vardy

2011

IEEE Trans. Inform. Theory

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“…Since the definition of the RLL constraint in [12] and [13], several variants to the RLL constraint were suggested. However, the basic premise that we may use ever growing runs of 's until we reach a run length for which the clock drift may produce a spurious or missing , was never changed.…”

Section: Hementioning

confidence: 99%

On the Capacity of the Precision-Resolution System

Schwartz

Bruck

2010

IEEE Trans. Inform. Theory

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Abstract-Arguably, the most prominent constrained system in storage applications is the (d; k)-run-length limited (RLL) system, where every binary sequence obeys the constraint that every two adjacent 1's are separated by at least d consecutive 0's and at most k consecutive 0's, namely, runs of 0's are length limited. The motivation for the RLL constraint arises mainly from the physical limitations of the read and write technologies in magnetic and optical storage systems. We revisit the rationale for the RLL system, reevaluate its relationship to the constraints of the physical media and propose a new framework that we call the Precision-Resolution (PR) system. Specifically, in the PR system there is a separation between the encoder constraints (which relate to the precision of writing information into the physical media) and the decoder constraints (which relate to its resolution, namely, the ability to distinguish between two different signals received by reading the physical media). We compute the capacity of a general PR system and compare it to the traditional RLL system. Index Terms-Run-length limited (RLL), constrained coding, capacity of constrained channels.

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“…1993, Tang and Bahl 1970, Norris and Bloomberg 1981. In this paper, several theorems relating characteristic equations and values of channel capacity between minimum bandwidth and DC-free sequences are developed.…”

Section: Botha Et Almentioning

confidence: 99%

The transformation of line codes

Botha¹,

Menyennett²,

Ferreira³

1994

International Journal of Electronics

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Theorems relating characteristic equations and values of channel capacity of some classes of constrained sequences to other classes are presented. These results provide new characteristic equations which can be used for the calculation of channel capacity, and enable existing tables containing values of channel capacity for constrained sequences to be used to find previously unknown values of capacity for other classes of sequences. Algorithms for transforming DC-free line codes and their decoders to minimum bandwidth line codes, and vice-versa, are presented. These algorithms are then used to obtain two new minimum bandwidth line codes.

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Block codes for a class of constrained noiseless channels

Cited by 156 publications

References 6 publications

New Bounds on the Capacity of Multidimensional Run-Length Constraints

New Bounds on the Capacity of Multidimensional Run-Length Constraints

On the Capacity of the Precision-Resolution System

The transformation of line codes

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