Title :
On the Power Spectral Density of Constrained Sequences
Author :
Pimentel, Cecilio ; Rocha, Valdemar C da, Jr.
Author_Institution :
Dept. of Electron. & Syst., Univ. Fed. de Pernambuco, Recife
fDate :
3/1/2007 12:00:00 AM
Abstract :
This paper derives a simple closed-form expression for computing the power spectral density (PSD) of constrained sequences whose constraints are characterized by a function of an ergodic Markov process specified in terms of a Mealy machine. A suitable matrix description of the stochastic behavior of the constrained sequence is used to express its autocorrelation sequence in a compact matrix form that simplifies the calculation of the PSD. Examples of the application of this technique in cases of practical interest are provided, including differentially encoded binary sequences, source-driven binary Huffman codes, maximum entropy (d,k) codes, and convolutional- or block-encoded sequences. A unified treatment to several widely used constrained sequences is provided
Keywords :
Huffman codes; Markov processes; binary codes; binary sequences; block codes; convolutional codes; correlation methods; matrix algebra; maximum entropy methods; sequential codes; source coding; Mealy machine; autocorrelation sequence; block-encoded sequences; constrained sequences; convolutional-encoded sequences; differentially encoded binary sequences; ergodic Markov process; maximum entropy codes; power spectral density; source-driven binary Huffman codes; Autocorrelation; Brazil Council; Closed-form solution; Entropy; Fourier transforms; Hidden Markov models; Markov processes; Pulse modulation; Signal processing; Stochastic processes; Autocorrelation function; Fourier transform; Markov chain; Mealy machine; Moore machine; power spectral density (PSD);
Journal_Title :
Communications, IEEE Transactions on
DOI :
10.1109/TCOMM.2007.892443
