On Noise Effect And Stochastic Resonance In Information Transmission

Random noise usually impairs the performance of linear systems,so it should be filtered.However,in some nonlinear systems,noise may help to enhance the response of systems.And it even plays an important role in optimizing the performance.Such a counter-intuitive phenomenon is termed stochastic resonance(SR).In the framework of information theory,this dissertation examines the effect of noise in information transmission and information processing,and shows the existence and applicability of SR.The main contributions are as follows.(1)In the discrete source scenario,noise enhancing mutual information in the single threshold system is discussed,and the SR effect is studied.This dissertation first focuses on the general M-ary input signal.In this case,the optimal noise which leads to the maximal mutual information is derived.And then,binary input signal is taken into consideration.The specific optimal noise is presented,and the maximal mutual information induced by such noise is shown to be equal to the entropy of the source.Moreover,when the noise is restricted to generalized Gaussian or binary symmetric ones,the parameter of noise is optimized so that suboptimal noises can be obtained.The corresponding noise-enhanced effects are displayed as well.Furthermore,the difference of effects among various suboptimal noises is analyzed.(2)In the continuous source scenario,noise-enhanced effects on mutual information in threshold systems are studied.In a single threshold system,it is found that the optimal noise is a constant one.Besides,some suboptimal noises and their effects are also obtained with optimization methods.However,the existence of suboptimal noises depends on the threshold.For example,when the threshold is rather small,the suboptimal noise may deteriorate to zero.As a result,the threshold of thresholds is defined to determine the existence of suboptimal noises.Specifically,when the system's threshold exceeds the threshold of thresholds,suboptimal noises exist and can improve mutual information.On the contrary,when system's threshold is set to be smaller than the threshold of thresholds,these predetermined noises cannot help improve mutual information.Moreover,the single threshold system is extended to an array of threshold units,in which case the SR effects of optimal and suboptimal noises are shown as well.(3)Measured by mean square error(MSE)distortion,SR phenomenon in scalar quantizing is explored.An SR quantizer is constructed,which consists of an array of binary quantizers and a linear decoder.First,according to Gateaux differential,the optimal noise in the array is shown to be a uniform one.At the same time,the minimal distortion induced by the optimal noise is obtained.And then,some other noises,including uniform noise with zero mean,Gaussian noise,Laplacian noise,and discrete noise,are also used to improve the performance of the SR quantizer.In the case that the granular region is fixed,the SR effects of various noises are shown for comparison.Finally,when the granular region can be optimized,better quantization performance may be acquired.Especially in the high rate case,the MSE distortion induced by the optimal noise can approximate zero.(4)Based on vector quantization,noise-enhanced effect on quantization performance is investigated.Two types of signal are considered,which are two-dimensional uniform signal and two-dimensional Gaussian signal.For each signal,this dissertation adopts two decoding schemes,i.e.,modified linear decoding and MAP decoding.And then,how uniform noise affects the MSE distortion is discussed.The results show that the distortion achieves the minimum when noise intensity is not zero.That is to say,SR occurs in vector quantization scenario.Furthermore,this dissertation compares the quantization performance enhanced by noise in such a vector quantizing case with that in the scalar case.In modified linear decoding scenario,it is found that when system's threshold is a little large or the number of threshold units is moderate,the distortion in vector quantizing is lower than that in the scalar case.It shows the superiority of vector quantizing.However,under some condition(e.g.,threshold is small and the number of threshold units is large),since the designed decoding scheme is simple,the noise-induced performance of vector quantization may be a little worse than that of scalar quantization.While in MAP decoding scenario,as quantization performance is enhanced by noise,vector quantization is always superior to scalar quantization.(5)Measured by bit error rate(BER),SR phenomenon in channel coding is explored.An array of threshold units is viewed as a channel,over which codewords are sent to the receiver.And the noise in the channel is assumed to be Gaussian.First,convolutional coding is employed.Based on the logarithmic maximum a posteriori probability(log-MAP)algorithm,decoding performance in the presence of Gaussian noise is evaluated by simulation;and SR can be observed.Next,the parallel concatenated turbo coding is paid attention to.For different numbers of threshold units and different threshold levels,Gaussian noise's effects on iterative turbo decoding are examined.In subthreshold scenario(i.e.,system's threshold is higher than the amplitude of codes),noise can help to improve BER performance of iterative decoding.Especially when noise intensity lies within the optimal region,BER may approximate to zero after a few decoding iterations.In addition,the larger the number of threshold units is,the more remarkable the decoding performance becomes.On the other hand,in suprathreshold scenario(i.e.,threshold is lower than the amplitude of codes),Gaussian noise is detrimental to turbo decoding.It means that SR does not exist in such a case.However,if Gaussian mixture noise is introduced into the array,noise will enhance decoding performance indeed.That is to say,suprathreshold stochastic resonance(SSR)occurs,and Gaussian mixture noise has an SSR effect on turbo decoding.These results above have shown the effects of random noise in information transmission,which may enrich the studies on SR.In some degree,this dissertation will enhance the consolidation of SR theory and information theory.