## No full-text available

To read the full-text of this research,

you can request a copy directly from the authors.

We find an analytic expression for the maximum of the normalized
entropy -Σ<sub>iεT</sub>p<sub>i</sub>ln
p<sub>i</sub>/Σ<sub>iεT</sub>ip<sub>i</sub> where the set T
is the disjoint union of sets S<sub>n</sub> of positive integers that
are assigned probabilities P<sub>n</sub>, Σ<sub>n</sub>P<sub>n
</sub>=1. This result is applied to the computation of the capacity of
weakly (d,k)-constrained sequences that are allowed to violate the
(d,k)-constraint with small probability

To read the full-text of this research,

you can request a copy directly from the authors.

Upper and lower bounds are presented for the capacity of weakly constrained two-dimensional codes. The maximum entropy is calculated for two simple models of 2-D codes constraining the probability of neighboring 1s as an example. For given models of the coded data, upper and lower bounds on the capacity for 2-D channel models based on occurrences of neighboring 1s are considered.

We find an analytic expression for the maximum of the normalized
entropy -Σ<sub>i∈T</sub>p<sub>i</sub> ln
p<sub>i</sub>/Σ<sub>i∈T</sub>ip<sub>i</sub> where the set T
is the disjoint union of sets S<sub>n</sub> of positive integers that
are assigned probabilities P<sub>n</sub>, Σ<sub>n</sub>P<sub>n
</sub>=1. This result is applied to the computation of the capacity of
weakly (d,k)-constrained sequences that are allowed to violate the
(d,k)-constraint with small probability

The author reports on the performance of a new class of
constrained codes, called weakly constrained codes. These codes do not
strictly guarantee the imposed channel constraints, but rather generate
codewords that violate, with a given (small) probability, the prescribed
constraint. Weakly constrained codes are specifically of interest when
it is desirable that the code rate R=p/q is very high, requiring
codewords of length q>100

Bell System Technical Journal, also pp. 623-656 (October)

Associate Editor for Coding theory. Publisher Item Identifier S

- R M Communicated
- Roth

communicated by R. M. Roth, Associate Editor for Coding theory. Publisher Item Identifier S 0018-9448(00)03101-1.

Constrained coding is a special kind of channel coding in which unconstrained user sequences are encoded into sequences that are required to satisfy certain hard constraints such as runlength limits

- I Introduction

I. INTRODUCTION
Constrained coding is a special kind of channel coding in which
unconstrained user sequences are encoded into sequences that are required to satisfy certain hard constraints such as runlength limits [10],
[14], [13].
Manuscript received December 29, 1998.
J. J. Ashley is with Infineon Technologies, Santa Cruz, CA 95060 USA
(e-mail: Jonathan.Ashley@infineon.com).

CA 95120 USA (e-mail: marcus@almaden.ibm.com)

- B H Marcus Is With Ibm Almaden Research
- San Center
- Jose

B. H. Marcus is with IBM Almaden Research Center, San Jose, CA 95120
USA (e-mail: marcus@almaden.ibm.com).
communicated by R. M. Roth, Associate Editor for Coding theory.
Publisher Item Identifier S 0018-9448(00)03101-1.