Neural encoding and decoding focus on the question: " What does the response of a neuron tell us about a stimulus ". In this chapter we consider a related but different question: " How much does the neural response tell us about a stimulus ". The techniques of information theory allow us to answer this question in a quantitative manner. Furthermore, we can use them to ask what forms of neural r...

Iterative decoding of two-dimensional systematic convolutional codes has been termed “turbo” (de)coding. Using log-likelihood algebra, we show that any decoder can he used which accepts soft inputs-including a priori values-and delivers soft outputs that can he split into three terms: the soft channel and a priori inputs, and the extrinsic value. The extrinsic value is used as an a priori value...

We are interested in the analysis and optimization of Raptor codes under a joint decoding framework, that is, when the precode and the fountain code exchange soft information iteratively. We develop an analytical asymptotic convergence analysis of the joint decoder, derive an optimization method for the design of efficient output degree distributions, and show that the new optimized distributio...

A recent paper demonstrated that the pattern of firing rates across ∼100 neurons in the anterior medial face patch is closely related to which human face (of 2,000) had been presented to a monkey [Chang L, Tsao DY (2017) Cell 169:1013-1028]. In addition, the firing rates for these neurons can be predicted for a novel human face. Although it is clear from this work that the firing rates of these...

Arithmetic coding, in conjunction with a suitable probabilistic model, can provide nearly optimal data compression. In this article we analyze the effect that the model and the particular implementation of arithmetic coding have on the code length obtained. Periodic scaling is often used in arithmetic coding implementations to reduce time and storage requirements; it also introduces a recency e...

the estimate of entropy (sample entropy), has been introduced by vasicek (1976), for the first time. in this paper, we provide an estimate of entropy of order statistics, that is the extention of the entropy estimate. then we present an application of the entropy estimate of order statistics as a test statistic for symmetry of distribution versus skewness. the proposed test has been compared wi...

We introduce a stop-code tolerant (SCT) approach to training recurrent convolutional neural networks for lossy image compression. Our methods introduce a multi-pass training method to combine the training goals of high-quality reconstructions in areas around stop-code masking as well as in highly-detailed areas. These methods lead to lower true bitrates for a given recursion count, both preand ...

In this report, the research conducted on entanglement in topological phases is detailed and summarized. This includes background developed and an explanation of the structure of the code written it MATLAB to compute various aspects of entanglement for topological systems. Topological phases are generally those that cannot be described by Landau symmetry-breaking, including the fractional quant...

A scientific problem described within a given code is mapped by a corresponding computational problem, We call complexity (algorithmic) the bit length of the shortest instruction which solves the problem. Deterministic chaos in general affects a dynamical systems making the corresponding problem experimentally and computationally heavy, since one must reset the initial conditions at a rate high...