scholarly journals The Positive Capacity Region of Two-Dimensional Run-Length-Constrained Channels

2006 ◽  
Vol 52 (11) ◽  
pp. 5128-5140 ◽  
Author(s):  
K. Censor ◽  
T. Etzion
Keyword(s):  
Two Dimensional ◽  
Capacity Region ◽  
Run Length ◽  
Positive Capacity

scholarly journals Lozenge tiling constrained codes

2014 ◽  
Vol 27 (4) ◽  
pp. 521-542 ◽  
Author(s):  
Bane Vasic ◽  
Anantha Krishnan
Keyword(s):  
Triangular Lattice ◽  
Constrained Systems ◽  
Square Lattice ◽  
Theoretical Treatment ◽  
Two Dimensional ◽  
Run Length ◽  
One Dimensional ◽  
Constrained Codes ◽  
Capacity Bounds ◽  
Decoder Design

While the field of one-dimensional constrained codes is mature, with theoretical as well as practical aspects of code- and decoder-design being well-established, such a theoretical treatment of its two-dimensional (2D) counterpart is still unavailable. Research has been conducted on a few exemplar 2D constraints, e.g., the hard triangle model, run-length limited constraints on the square lattice, and 2D checkerboard constraints. Excluding these results, 2D constrained systems remain largely uncharacterized mathematically, with only loose bounds of capacities present. In this paper we present a lozenge constraint on a regular triangular lattice and derive Shannon noiseless capacity bounds. To estimate capacity of lozenge tiling we make use of the bijection between the counting of lozenge tiling and the counting of boxed plane partitions.

scholarly journals Lossless Text Image Compression using Two Dimensional Run Length Encoding

2020 ◽  
Vol 4 (2) ◽  
pp. 75 ◽  
Author(s):  
Hilal H Nuha
Keyword(s):  
Image Compression ◽  
Compression Ratio ◽  
Data Communication ◽  
Binary Image ◽  
Huffman Coding ◽  
Two Dimensional ◽  
Run Length ◽  
Last Stage ◽  
Text Images ◽  
Scanned Documents

Text images are used in many types of conventional data communication where texts are not directly represented by digital character such as ASCII but represented by an image, for instance facsimile file or scanned documents. We propose a combination of Run Length Encoding (RLE) and Huffman coding for two dimensional binary image compression namely 2DRLE. Firstly, each row in an image is read sequentially. Each consecutive recurring row is kept once and the number of occurrences is stored. Secondly, the same procedure is performed column-wise to the image produced by the first stage to obtain an image without consecutive recurring row and column. The image from the last stage is then compressed using Huffman coding. The experiment shows that the 2DRLE achieves a higher compression ratio than conventional Huffman coding for image by achieving more than 8:1 of compression ratio without any distortion.

scholarly journals Zero Capacity Region of Multidimensional Run Length Constraints

10.37236/1465 ◽  
1999 ◽  
Vol 6 (1) ◽  
Author(s):  
Hisashi Ito ◽  
Akiko Kato ◽  
Zsigmond Nagy ◽  
Kenneth Zeger
Keyword(s):  
Binary Sequence ◽  
Capacity Region ◽  
Run Length ◽  
One Dimensional ◽  
Coordinate Axis ◽  
Length Constraint ◽  
Zero Capacity ◽  
The One ◽  
Constrained Capacity

For integers $d$ and $k$ satisfying $0 \le d \le k$, a binary sequence is said to satisfy a one-dimensional $(d,k)$ run length constraint if there are never more than $k$ zeros in a row, and if between any two ones there are at least $d$ zeros. For $n\geq 1$, the $n$-dimensional $(d,k)$-constrained capacity is defined as $$C^{n}_{d,k} = \lim_{m_1,m_2,\ldots,m_n\rightarrow\infty} {{\log_2 N_{m_1,m_2,\ldots ,m_n}^{(n; d,k)}} \over {m_1 m_2\cdots m_n}} $$ where $N_{m_1,m_2,\ldots ,m_n}^{(n; d,k)}$ denotes the number of $m_1\times m_2\times\cdots\times m_n$ $n$-dimensional binary rectangular patterns that satisfy the one-dimensional $(d,k)$ run length constraint in the direction of every coordinate axis. It is proven for all $n\ge 2$, $d\ge1$, and $k>d$ that $C^{n}_{d,k}=0$ if and only if $k=d+1$. Also, it is proven for every $d\geq 0$ and $k\geq d$ that $\lim_{n\rightarrow\infty}C^{n}_{d,k}=0$ if and only if $k\le 2d$.

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