Runlength codes from source codes

Kerpez, K.J.

doi:10.1109/18.79932

Cited by 10 publications

(4 citation statements)

References 15 publications

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“…Let the minimal set contain K words. One complete extension of this minimal set is comprised of the K 2 codewords formed by concatenating all words in the minimal set with each of the K words in the minimal set [6]; the next complete extension involves extending all K 2 words in a similar manner. In contrast, a partial extension of a minimal set is formed by selecting any one of the words and appending to it all K words from the minimal set [3].…”

Section: Minimal Sets and Their Extensionmentioning

confidence: 99%

Simplified search and construction of capacity‐approaching variable‐length constrained sequence codes

Steadman

Fair

2016

IET Communications

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Section: Minimal Sets and Their Extensionmentioning

confidence: 99%

Simplified search and construction of capacity‐approaching variable‐length constrained sequence codes

Steadman

Fair

2016

IET Communications

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“…Dyadic PMFs resulting from source codes are in general not optimal. For the (d, k) constrained noiseless channel, it was claimed in [3] that a source code asymptotically achieves capacity. To the best of our knowledge, for DMCs, there exist no results in the literature on optimality and asymptotic behavior of dyadic PMFs.…”

Section: Introductionmentioning

confidence: 99%

Matching Dyadic Distributions to Channels

Böcherer

Mathar

2011

2011 Data Compression Conference

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Many communication channels with discrete input have non-uniform capacity achieving probability mass functions (PMF). By parsing a stream of independent and equiprobable bits according to a full prefix-free code, a modulator can generate dyadic PMFs at the channel input. In this work, we show that for discrete memoryless channels and for memoryless discrete noiseless channels, searching for good dyadic input PMFs is equivalent to minimizing the Kullback-Leibler distance between a dyadic PMF and a weighted version of the capacity achieving PMF. We define a new algorithm called Geometric Huffman Coding (GHC) and prove that GHC finds the optimal dyadic PMF in O(m log m) steps where m is the number of input symbols of the considered channel. Furthermore, we prove that by generating dyadic PMFs of blocks of consecutive input symbols, GHC achieves capacity when the block length goes to infinity.

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“…The idea of constructing (d, k)-codes from source codes is not new. For example, by reversing a source encoder-decoder pair, the decoder of a suitable source code can be used to encode unconstrained Bernoulli(1/2)-distributed bitstreams into (d, k)-sequences in a recoverable manner [3], [4]. In such designs, the choice of source code is guided by special properties of (d, k)sequences with maximum-entropy (maxentropic) distribution.…”

Section: Introductionmentioning

confidence: 99%

“…Intuitively speaking, it better conforms the data to the characteristics of maxentropic sequences. It is also worth noting that the binary DT is a special case of general DT's, such as the ones introduced in [3], [4]. In fact, some of these source coding techniques can be readily applied to the binary case, where a Bernoulli(p) distribution replaces Λ d,k .…”

Section: Introductionmentioning

confidence: 99%

Optimal Parsing Trees for Run-Length Coding of Biased Data

Aviran

Siegel

Wolf

2006

2006 IEEE International Symposium on Information Theory

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We study coding schemes which encode unconstrained sequences into run-length-limited (d, k)-constrained sequences. We present a general framework for the construction of such (d, k)-codes from variable-length source codes. This framework is an extension of the previously suggested bit stuffing, bit flipping and symbol sliding algorithms. We show that it gives rise to new code constructions which achieve improved performance over the three aforementioned algorithms. Therefore, we are interested in finding optimal codes under this framework, optimal in the sense of maximal achievable asymptotic rates. However, this appears to be a difficult problem. In an attempt to solve it, we are led to consider the encoding of unconstrained sequences of independent but biased (as opposed to equiprobable) bits. Here, our main result is that one can use the Tunstall source coding algorithm to generate optimal codes for a partial class of (d, k) constraints.

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Runlength codes from source codes

Cited by 10 publications

References 15 publications

Simplified search and construction of capacity‐approaching variable‐length constrained sequence codes

Simplified search and construction of capacity‐approaching variable‐length constrained sequence codes

Matching Dyadic Distributions to Channels

Optimal Parsing Trees for Run-Length Coding of Biased Data

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