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Nested input-constrained codes

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3 Author(s)
J. Hogan ; Hewlett-Packard Co., Palo Alto, CA, USA ; R. M. Roth ; G. Ruckenstein

An input-constrained channel, or simply a constraint, is a set S of words that is generated by a finite 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 finite-state 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. Specifically, given two constraints S1 and S 2 such that S1⊆S2 and two described rates, conditions are provided for the existence of respective deterministic finite-state encoders ε1 and ε2 , at the given rates, such that (the state diagram of) ε1 is a subgraph of ε2 Such encoders are referred to as nested encoders. The provided conditions are also constructive in that they imply an algorithm for finding such encoders when they exist. The nesting structure allows to decode ε1 while using the decoder of ε2. Developments in optical recording suggest a potential application that can take a significant advantage of nested encoders

Published in:

IEEE Transactions on Information Theory  (Volume:46 ,  Issue: 4 )