The Models Of Encoding And Decoding In Neuronal Population

Encoding and decoding in neuronal population is the key issue in neural information processing.In this paper,we first introduce firing rate and spikes-count rate to describe the neurons response to external stimuli,and obtain the tuning curve of firing rate according to the recorded spike activities.Base on the phase description of neuronal oscillator,we get the averaged neuronal firing rate under stimulus phase,with correlations and noise environment in neural system,we establish the encoding model of neuronal population activities and extend to continuous form. By the analysis and simulation, we found that the Fisher information slowly decreases and then fast increases with the effective phase width, and the larger neuronal density,the more Fisher information we can see.We also found the minimum error of the population coding decreases with the neuronal density, so the accuracy realization in population coding depends on the scale of neuronal population.We present the fundmental principle of neuronal population decoding,the Bayesian rule,using maximum likelihood inference(MLI)to analyse the efficiency of faithful model,unfaithful model and the model of center of mass,and compare the performance among these models by simulation.Aa a result,we found the decoding error of FMLI(MLI based on faithful model) is better than UMLI's(MLI based on unfaithful model),and the decoding error varies with effective phase width and neuronal density is as the same as Fisher information.when the neuronal density is fairly large,UMLI and FMLI have the similar decoding performance,so the UMLI can make a good compromise between decoding accuracy and computational costs.Finally,we give the SBD(sequential Bayesian decoding)method based on MLI and MAP(maximize a posteriori),assuming the estimation of stimuli in each decoding step as the prior in the following decoding procedure,and investigate how the error varies in each decoding step.The results shows the optimal decoding error which we can acquire, is just the decoding error in the first step devided by the number of decoding steps.we can conclude the accumulation of the prior is the guarantee of population decoding accuracy,it may be a little enlightment to reveal the function of the brain.