Timo Koski

Population models with environmental stochasticity

Two discrete population models, one with stochasticity in the carrying capacity and one with stochasticity in the per capita growth rate, are investigated. Conditions under which the corresponding Markov processes are null recurrent and positively recurrent are derived.

Classification of Enterobacteriaceae by minimization of stochastic complexity

A new method for classifying bacteria is presented and applied to a large set of biochemical data for the Enterobacteriaceae. The method minimizes the bits needed to encode the classes and the items or, equivalently, maximizes the information content of the classification. The resulting taxonomy of Enterobacteriaceae corresponds well to the general structure of earlier classifications. Minimization of stochastic complexity can be considered as a useful tool to create bacterial classifications that are optimal from the point of view of information theory.

Minimum entropy of error principle in estimation

Abstract The principle of minimum error entropy estimation as found in the work of Weidemann and Stear is reformulated as a problem of finding optimum locations of probability densities in a given mixture such that the resulting (differential) entropy is minimized. New results concerning the entropy lower bound are derived. Continuity of the entropy and attaining the minimum entropy are proved in the case where the mixture is finite. Some other examples and situations, in particular that of symmetric unimodal densities, are studied in more detail.

Some properties of generalized exponential entropies with applications to data compression

Abstract The scale of exponential entropies of order (α, β) is introduced. It unifies a number of notions of (generalized) differential entropies for continuous distributions. The properties of this scale are derived from results in the theory of means. We show that the scale can represent the extent of a probability distribution, i.e. its degree of concentration with regard to a reference measure. This fact has several consequences that are of interest in the theory of data (or signal) compression. The aspects of data compression considered are the intrinsic extent of a probability distribution, introduced by L. L. Campbell, and the properties of entropy series. We investigate specially the exponential families of distributions, in particular the Miller-Thomas (or generalized Gaussian) family of distributions.

Combined linear-Viterbi equalizers-a comparative study and a minimax design

Combined linear-Viterbi equalizer (CLVE) is a term often used for a class of digital receivers reducing the complexity of the Viterbi detector by assuming an approximate channel model together with linear pre-equalization of the received data. The authors reconsider a weighted least squares design technique for CLVEs by introducing a minimax criterion for suppressing the strongest component of the residual intersymbol interference. Odling (1993) studied the performance of some proposed CLVE design methods and evaluated them by simulated bit error rates. The present authors investigate the performance of the minimax design and of the CLVE designs found in literature for two GSM test channels. They also present a comparison of the CLVE designs based on a common quadratic optimization criterion for the selection of the channel prefilter and the desired impulse response.<<ETX>>

Minimum entropy of error estimation for discrete random variables

The principle of minimum entropy of error estimation (MEEE) is formulated for discrete random variables. In the case when the random variable to be estimated is binary, we show that the MEEE is given by a Neyman-Pearson-type strictly monotonous test. In addition, the asymptotic behavior of the error probabilities is proved to be equivalent to that of the Bayesian test.

On quantizer distortion and the upper bound for exponential entropy

A sharp upper bound is derived for the exponential entropy in the class of absolutely continuous distributions with specific standard deviation and an exact description of the extremal distributions. This result is interpreted as determining the least favorable cases for certain methods of quantization of analog sources. It is known that for a large class of quantizers (both zero-memory and vector) the rth power distortion, as well as some other distortion criteria, are bounded below by a constant, depending on r, multiplied by a certain integral of the sources probability density. It is pointed out that this bound can be rewritten in terms of the exponential entropy. The exponential entropy measures the quantitative extent or range of the source distribution. This fact gives a physical interpretation of the indicated limits of quantizer performance, further elucidated by the main result. >

Statistics of the binary quantizer error in single-loop sigma-delta modulation with white Gaussian input

Representations and statistical properties of the process e¯ defined by e¯n+1=λ(e¯n+ξn ), are given. Here λ(u):=u-b·sign(u)+m and {ξn}n=0+∞ is Gaussian white noise. The process e¯ represents the binary quantizer error in a model for single-loop sigma-delta modulation. The innovations variables are found and the existence and uniqueness of an invariant probability measure, ergodicity properties, as well as the existence of the exponential moment with respect to the invariant probability are proved using Markov process theory. We consider also e¯ as a random perturbation, for small values of the variance of ξn, Of the orbits of sn+1=λ(sn). Here sn has the uniform invariant distribution on the interval [m-h, m+b]. Analytical approximations to the structure of the power spectrum of e¯ are obtained using a linear prediction in terms of the innovations variables and the perturbation approach

Clustering and quantization of binary vectors with stochastic complexity

Stochastic complexity (SC) is used for determining both the codebook and its size in a vector quantizer for binary strings given a training sequence.<<ETX>>

A genie-aided detector with a probabilistic description of the side information

Building on Forneys concept of the genie (1972), and introducing the idea of an explicit statistical description of the side information provided to the genie-aided detector, we develop a generic tool for derivation of lower bounds on the bit-error rate of any actual receiver. With this approach, the side information statistics become design parameters, which may be chosen to give the resulting bound a desired structure. To illustrate this, we choose statistics in order to obtain a special case: the lower bound derived by Mazo (1975). The statistical description of the side information makes the lower bounding a transparent application of Bayesian theory.