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Task-driven intra- and interarea communications in primate cerebral cortex

Significance How do multiple neurons communicate to solve a cognitive task? To answer this question, we investigate spike-train directional correlations across five primate cortical areas simultaneously recorded during a somatosensory discrimination task. Correlations are inferred using a nonparametric procedure that models spike trains as Markovian binary series and dynamically estimates the directed information between every neuron pair at different delays. We find that information processing during the discrimination task can be described by intra- and interarea decision-driven delayed correlations, which are no longer found when a monkey receives both stimuli but does not perform the task. Neural correlations during a cognitive task are central to study brain information processing and computation. However, they have been poorly analyzed due to the difficulty of recording simultaneous single neurons during task performance. In the present work, we quantified neural directional correlations using spike trains that were simultaneously recorded in sensory, premotor, and motor cortical areas of two monkeys during a somatosensory discrimination task. Upon modeling spike trains as binary time series, we used a nonparametric Bayesian method to estimate pairwise directional correlations between many pairs of neurons throughout different stages of the task, namely, perception, working memory, decision making, and motor report. We find that solving the task involves feedforward and feedback correlation paths linking sensory and motor areas during certain task intervals. Specifically, information is communicated by task-driven neural correlations that are significantly delayed across secondary somatosensory cortex, premotor, and motor areas when decision making takes place. Crucially, when sensory comparison is no longer requested for task performance, a major proportion of directional correlations consistently vanish across all cortical areas.

Bayesian

Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy et al.; the second expression is a function of an information-spectrum measure and implies the tightness of a generalized Verdú-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose.

M

Random-coding exact characterizations and bounds to the error probability of joint source-channel coding are presented. In particular, upper bounds using maximum-a-posteriori and threshold decoding are derived as well as a lower bound motivated by Verdú-Hans lemma.

-Ary Hypothesis Testing: The Meta-Converse and Verdú-Han Bounds Are Tight

This paper studies the random-coding exponent of joint source-channel coding for a scheme where source messages are assigned to disjoint subsets (referred to as classes), and codewords are independently generated according to a distribution that depends on the class index of the source message. For discrete memoryless systems, two optimally chosen classes and product distributions are found to be sufficient to attain the sphere-packing exponent in those cases where it is tight.

Random-coding joint source-channel bounds

We present a study of large multiple-access communication systems in which multiuser detection is performed without knowledge of the number of interferers. When the number of users increases without bound, optimum detectors can be analyzed asymptotically. A statistical physics approach based on spin glass theory provides analytical tools to deal with large systems in which the performance parameters to be analyzed (error probabilities, etc) are self-averaging in the limit. Of particular interest is the replica method that is used as a key technique to compute the free-energy function and the macroscopic parameters that determine the multiuser efficiency and the bit error probability in the large system limit.

A Derivation of the Source-Channel Error Exponent Using Nonidentical Product Distributions

We study a source-channel coding scheme in which source messages are assigned to classes and encoded using a channel code that depends on the class index. While each class code can be seen as a concatenation of a source code and a channel code, the overall performance improves on that of separate source-channel coding and approaches that of joint source-channel coding as the number of classes increases. The performance of this scheme is studied by means of random-coding bounds and validated by simulation of a low-complexity implementation using existing source and channel codes.

Large-System Analysis of Static Multiuser Detection with an Unknown Number of Users

Specifically, during the passive stimulation task there is an abrupt decrease in the number of causal correlations after the first stimulation, which is shown to be independent of the spike-train variability of each area. Conclusions Neuronal causal correlation paths that are specific to the discriminations task are ubiquitous, bidirectional and remain approximately constant along the task in both sensory and motor areas. These findings are robust to the stimulation pair under study and the spike-train variability of each area.

Source-channel coding with multiple classes

We derive a random-coding upper bound on the average probability of error of joint source-channel coding that recovers Csiszárs error exponent when used with product distributions over the channel inputs. Our proof technique for the error probability analysis employs a code construction for which source messages are assigned to subsets and codewords are generated with a distribution that depends on the subset.

Causal correlation paths across cortical areas in decision making

We analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver. Our main goal is to determine the performance loss caused by the need for estimating the identities of active users, which are not known a priori. To prevent a loss of optimality, we assume that identities and data are estimated jointly, rather than in two separate steps. We examine the performance of multiuser detectors when the number of potential users is large. Statistical-physics methodologies are used to determine the fixed-point equation whose solutions yield the multiuser efficiency of the optimal detector. Special attention is paid to the large signal-to-noise ratio, which yields tight closed-form bounds on the minimum mean-squared error. These bounds analytically illustrate the set of solutions of the fixed-point equation, and their relationship with the maximum system load. By identifying the region of computationally feasible solutions, we study the maximum load that the detector can support for a given SNR and quality of service, specified by the multiuser efficiency.

Achieving Csiszár's source-channel coding exponent with product distributions

This paper studies an almost-lossless source-channel coding scheme in which source messages are assigned to different classes and encoded with a channel code that depends on the class index. The code performance is analyzed by means of random-coding error exponents and validated by simulation of a low-complexity implementation using existing source and channel codes. While each class code can be seen as a concatenation of a source code and a channel code, the overall performance improves on that of separate source-channel coding and approaches that of joint source-channel coding when the number of classes increases.