Sequence-State Coding for Digital Transmission

Franaszek, P. A.

doi:10.1002/j.1538-7305.1968.tb00034.x

Cited by 137 publications

(42 citation statements)

References 2 publications

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“…Since we consider fixed length codes the size of t,he code is determined by the smallest set belonging to some state in the model. Franaszek [3] noted that if we take a subset of all states in the model and require the codewords to start and end in states of this subset then an optimum subset exists. This subset is known as the set of principal states and Franaszek descrihed an algorithm to search for these principal states.…”

Section: On T H E Principal State Methods For Rtjnlength Limited Sequementioning

confidence: 99%

On the principal state method for run-length limited sequences

Tjalkens

1994

IEEE Trans. Inform. Theory

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Citation for published version (APA):Tjalkens, T. J. (1994 Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publicationGeneral rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nl providing details and we will investigate your claim. Abstract. We present a det.ailed result on Franaszek's principal state method for the generation of runlength constrained codes. We show that, whenever the constraints k and d satisfy k 2 2d > 1, the set of "principal states" is so, S I , . . . , sk-1. Thns there is no need for Franaszek's search algorithm anymore. The connting technique used to obt,ain this result also shows thal. "state independent decoding" can he achieved using not more than three codewords per message and it allows us to compare the principal state method with other practical schemes originating from the work of Tang and Bahl and also allows us to m e an efficient enumerative coding implementation of the encoder and decoder.

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Section: On T H E Principal State Methods For Rtjnlength Limited Sequementioning

confidence: 99%

On the principal state method for run-length limited sequences

Tjalkens

1994

IEEE Trans. Inform. Theory

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“…There are many code construction method by which we can construct an encoder which encodes binary unconstrained sequences into binary sequences satisfying the constraint. For example, see [6], [7].…”

Section: Introductionmentioning

confidence: 99%

Insertion rate and optimization of redundancy of constrained systems with unconstrained positions

Kamabe

2009

2009 IEEE International Symposium on Information Theory

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Abstract-Immink and Cai have shown that the maxentropic bound for the Wijngaarden-Immink coding scheme is not tight. They have given simple bit-stuffing coding schemes whose code rates are greater than the bound. We analyze this problem in terms of finite state transition diagrams. Then we give a better bound of the code rate of the coding scheme and prove that our bound is better than the maxentropic bound when the insertion rate is 1/2.

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“…For each class of block-type-decodable encoders, it can be shown that there exists an ( )-encoder in class if and only if there exists such an encoder which is a subgraph of (in particular, this holds when is the Shannon cover) [11]. Thus, the problem of designing block-type-decodable encoders is equivalent to choosing a subgraph of , in particular, a subset of , called a set of principal states (this terminology goes back to Franaszek [2] who used it only for the class of deterministic encoders). It follows that and We do not know of a formula for as simple as those above, but, as with and , it is a function of only an arbitrary irreducible, deterministic presentation of the constraint, such as the Shannon cover.…”

Section: Block-type-decodable Encodersmentioning

confidence: 99%

“…However, this problem can be considerably more tractable for the class of deterministic encoders; these are finite-state encoders with deterministic output labeling. While deterministic encoders do not necessarily have good error propagation properties, it is well known that for RLL( ) constraints, the optimal rates of deterministic and block-decodable encoders coincide for every block length [2], [3], [5].…”

Section: Block-type-decodable Encodersmentioning

confidence: 99%

“…In Section II, we summarize some necessary background material on constrained coding. In Section III, we give formal definitions of the three classes of encoders that we consider, and we give, in principle, a description of how the optimal encoder of each type can be constructed using Franaszek's notion of a set of principal states [2], [3]. We give a complete proof of a sufficient condition, due to Franaszek, for the equality of the optimal rates of block-decodable and deterministic encoders.…”

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Optimal block-type-decodable encoders for constrained systems

Chaichanavong

Marcus²

2003

IEEE Trans. Inform. Theory

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Abstract-A constrained system is presented by a finite-state labeled graph. For such systems, we focus on block-type-decodable encoders, comprising three classes known as block, block-decodable, and deterministic encoders. Franaszek gives a sufficient condition which guarantees the equality of the optimal rates of block-decodable and deterministic encoders for the same block length. In this paper, we introduce another sufficient condition, called the straight-line condition, which yields the same result. Run-length limited RLL( ) and maximum transition run MTR( ) constraints are shown to satisfy both conditions. In general, block-type-decodable encoders are constructed by choosing a subset of states of the graph to be used as encoder states. Such a subset is known as a set of principal states. For each type of encoder and each block length, a natural problem is to find a set of principal states which maximizes the code rate. We show how to compute the asymptotically optimal sets of principal states for deterministic encoders and how they are related to the case of large but finite block lengths. We give optimal sets of principal states for MTR( )-block-type-decodable encoders for all codeword lengths. Finally we compare the code rate of nonreturn to zero inverted (NRZI) encoders to that of corresponding nonreturn to zero (NRZ) and signed NRZI encoders.

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Sequence-State Coding for Digital Transmission

Cited by 137 publications

References 2 publications

On the principal state method for run-length limited sequences

On the principal state method for run-length limited sequences

Insertion rate and optimization of redundancy of constrained systems with unconstrained positions

Optimal block-type-decodable encoders for constrained systems

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