Construction of FSSM Modeled Encoders to Meet Specific Spectral Requirements

Yongguang ZHU  Ivan J. FAIR  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A   No.9   pp.1772-1779
Publication Date: 2007/09/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.9.1772
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
channel constraints,  constrained sequence coding,  PSD,  Fourier series,  FSSM,  state transition,  autocorrelation,  autocovariance,  

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In digital transmission and storage systems, sequences must have attributes that comply with the physical characteristics of the channel. These channel constraints can often be satisfied through constrained sequence coding techniques which avoid use of sequences that violate the given channel constraints. In the design of a constrained code, it is usually helpful to consider the PSD of the encoded sequence in order to ensure that PSD requirements are met, and to obtain an indication of bandwidth, response at dc, average power peaks, and other spectral characteristics of interest. In this paper, we introduce an approach for the construction of finite-state sequential machine (FSSM) modeled encoders to satisfy spectral requirements. This approach involves construction of either a Mealy or a Moore FSSM to represent the encoder, and evaluation of the state transition probabilities and codeword values such that the PSD of the designed code meets a predefined spectral shape. Examples in this paper demonstrate the usefulness of this approach.