Lower bounds on the anticipation of encoders for input-constrained channels

Ruckenstein, G.; Roth, Ron M.

doi:10.1109/18.930919

Cited by 2 publications

(1 citation statement)

References 14 publications

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“…! v` (11) in E that generates a word a 1 a 2 : : : a`whose su x is w 0 . Write w = a ?m+1 a ?m+2 : : : a 0 , and denote by w j the word a j?m+1 a j?m+2 : : : a j .…”

Section: Conditions For Having Deterministic Nested Encodersmentioning

confidence: 99%

Nested input-constrained codes

Hogan

Roth²,

Ruckenstein³

2000

IEEE Trans. Inform. Theory

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An input-constrained channel, or simply a constraint, is a set S of words that is generated by a nite labeled directed graph. An encoder for S maps in a lossless manner sequences of unconstrained input blocks into sequences of channel blocks, the latter sequences being words of S. In most applications, the encoders are nitestate machines and, thus, presented by state diagrams. In the special case where the state diagram of the encoder is (output) deterministic, only the current encoder state and the current channel block are needed for the decoding of the current input block. In this work, the problem of designing coding schemes that can serve two constraints simultaneously is considered. Speci cally, given two constraints S 1 and S 2 such that S 1 S 2 and two prescribed rates, conditions are provided for the existence of respective deterministic nite-state encoders E 1 and E 2 , at the given rates, such that (the state diagram of) E 1 is a subgraph of E 2. Such encoders are referred to as nested encoders. The provided conditions are also constructive in that they imply an algorithm for nding such encoders when they exist. The nesting structure allows to decode E 1 while using the decoder of E 2. Recent developments in optical recording suggest a potential application that can take a signi cant advantage of nested encoders.

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“…! v` (11) in E that generates a word a 1 a 2 : : : a`whose su x is w 0 . Write w = a ?m+1 a ?m+2 : : : a 0 , and denote by w j the word a j?m+1 a j?m+2 : : : a j .…”

Section: Conditions For Having Deterministic Nested Encodersmentioning

confidence: 99%

Nested input-constrained codes

Hogan

Roth²,

Ruckenstein³

2000

IEEE Trans. Inform. Theory

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Parallel constrained coding with application to two-dimensional constraints

Halevy

Roth

2002

IEEE Trans. Inform. Theory

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A parallel constrained coding scheme is considered where p-blocks of raw data are encoded simultaneously into q tracks such that the contents of each track belong to a given constraint S. It is shown that as q increases, there are parallel block decodable encoders for S whose coding ratio, p=q, converges to the capacity of S. Examples are provided where parallel coding allows block decodable encoders, while conventional coding, at the same rate, does not. Parallel encoders are then applied as building blocks in the construction of block decodable encoders for certain families of two-dimensional constraints.

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Lower bounds on the anticipation of encoders for input-constrained channels

Cited by 2 publications

References 14 publications

Nested input-constrained codes

Nested input-constrained codes

Parallel constrained coding with application to two-dimensional constraints

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