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Bit stuffing algorithms and analysis for run length constrained channels in two and three dimensions
 IEEE TRANS. INFORM. THEORY
, 2004
"... A rigorous derivation is given of the coding rate of a variabletovariable length bitstuffing coder for a twodimensional (1)constrained channel. The coder studied is “nearly” a fixedtofixed length algorithm. Then an analogous variabletovariable length bitstuffing algorithm for the threedim ..."
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Cited by 8 (1 self)
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A rigorous derivation is given of the coding rate of a variabletovariable length bitstuffing coder for a twodimensional (1)constrained channel. The coder studied is “nearly” a fixedtofixed length algorithm. Then an analogous variabletovariable length bitstuffing algorithm for the threedimensional (1)constrained channel is presented, and its coding rate is analyzed using the twodimensional method. The threedimensional coding rate is demonstrated to be at least 0 502, which is proven to be within 4 % of the capacity.
Zero/Positive Capacities of TwoDimensional Runlength Constrained Arrays
 In Proc. 2001 IEEE Intl. Symp. on Inform. Theory
, 2004
"... A binary sequence satisfies a onedimensional (d 1 , k 1 , d 2 , k 2 ) runlength constraint if every run of zeroes has length at least d 1 and at most k 2 and every run of ones has length at least d 2 and at most k 2 . A twodimensional binary array is (d 1 , k 1 , d 2 , k 2 ; d 3 , k 3 , d 4 , k ..."
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Cited by 7 (1 self)
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A binary sequence satisfies a onedimensional (d 1 , k 1 , d 2 , k 2 ) runlength constraint if every run of zeroes has length at least d 1 and at most k 2 and every run of ones has length at least d 2 and at most k 2 . A twodimensional binary array is (d 1 , k 1 , d 2 , k 2 ; d 3 , k 3 , d 4 , k 4 ) constrained if it satisfies the onedimensional (d 1 , k 1 , d 2 , k 2 ) runlength constraint horizontally and the onedimensional (d 3 , k 3 , d 4 , k 4 ) runlength constraint vertically. For given d 1 , k 1 , d 2 , k 2 , d 3 , k 3 , d 4 , k 4 , the twodimensional capacity is defined as d 1 , k 1 , d 2 , k 2 ; d 3 , k 3 , d 4 , k 4 ) denotes the number of (d 1 , k 1 , d 2 , k 2 ; d 3 , k 3 , d 4 , k 4 ) constrained m n binary arrays. Such constrained systems can find application in twodimensional digital storage applications.
New Bounds on the Capacity of Multidimensional RunLength Constraints
, 2011
"... We examine the wellknown problem of determining the capacity of multidimensional runlengthlimited 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 o ..."
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Cited by 2 (2 self)
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We examine the wellknown problem of determining the capacity of multidimensional runlengthlimited 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 RLL systems. These bounds are better than all previouslyknown analytical bounds for , and are tight asymptotically. Thus, we settle the open question: what is the rate at which the capacity of RLL systems converges to 1 as ? We also provide the first nontrivial upper bound on the capacity of general RLL systems.
Constrained Codes for TwoDimensional Channels
, 2006
"... The research thesis was done under the supervision of Prof. Tuvi Etzion in the Department of Computer Science. I thank Prof. Tuvi Etzion for his devoted guidance. I thank little Ofek, Noga, Neta and Almog, for the light they shine. The generous financial help of the Technion is gratefully acknowledg ..."
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Cited by 1 (1 self)
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The research thesis was done under the supervision of Prof. Tuvi Etzion in the Department of Computer Science. I thank Prof. Tuvi Etzion for his devoted guidance. I thank little Ofek, Noga, Neta and Almog, for the light they shine. The generous financial help of the Technion is gratefully acknowledged.
IEEE TRANSACTIONS ON INFORMATION THEORY 1 Estimation
"... of the capacity of multidimensional constraints using the 1vertex transfer matrix ..."
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of the capacity of multidimensional constraints using the 1vertex transfer matrix
TimeSpace Constrained Codes for PhaseChange Memories
, 2012
"... Phasechange memory (PCM) is a promising nonvolatile solidstate 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, wh ..."
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Phasechange memory (PCM) is a promising nonvolatile solidstate 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 timespace constraint for PCM, which was originally proposed by Jiang et al. A code is called an (α,β,p)constrained code if for any α consecutive rewrites and for any segment of β contiguous cells, the total rewrite cost of the β cells over those α 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 (α � 1,β = 1,p = 1)constrained codes and show another construction for (α = 1,β � 1,p � 1)constrained codes. Finally, we show that these two constructions can be used to construct codes for all values of α, β, and p.