  # Gaussian mutual information homework

Like Liked. Madhumita Tamhane. Work is worship. Full Name Comment goes here. Are you sure you want to Yes No. Logeshwari Logeshwari. Show More. No Downloads. Views Total views. Actions Shares. No notes for slide. Information theory 1. Check if x is a complete probability scheme?

Find Entropy. Find entropy if all messages are equiprobable. Find rate of information, if source emits symbols once every milisecond. A discrete source emits one of the 5 symbols once every millisecond. Find information rate. In the Morse code, dash is represented by a current pulse of 3 unit duration and dot as 1 unit duration.

Calculate information content in single dot and dash. Calculate average information in dash-dot code. Assuming dot and pause between symbols are 1ms each, find average rate of information. Total 10 ms for 4 symbols. Show that entropy of source with equi-probable symbols in always maximum. One of permissible yj is received with given probability. This Conditional Entropy is the measure of information about the receiver where it is known that a particular Xi is transmitted.

It may be the result of one of the Xi with a given probability. This Conditional Entropy is the measure of information about the source where it is known that a particular Yj is received. It is the measure of equivocation or how well input content can be recovered from the output. Transmitter has an alphabet consisting of five letters x1, x2, x3, x4 , x5 And receiver has an alphabet consisting of four letters - y1, y2, y3, y4. Following probabilities are given. Find all entropies. Show that in discrete noise free channel both the conditional entropies are zero.

Entropy for discrete channel with independent input-output. Not desired. Try the other case too. Priori entropy of X. Is it due to transmission of xi? They are the properties of channel. If all the messages are equi- probable!! Find mutual information for noiseless channel. Rest remains same. Calculate I. Source is NOT equi- probable. Source is equi- probable. Channel in not useless. Rest combinations are erased. Toggle navigation. Homework 5 has been posted.

Homework 4 has been posted. Quiz on it will be held on Friday, November 8, pm. Homework 3 has been posted. Quiz on it will be held on Friday, October 4, pm. Homework 2 has been posted. Quiz on it will be held on Friday, September 20, pm. Please submit graphs for Q2 separately for grading by Monday, September Homework 1 has been posted.

Quiz on it will be held on Friday, September 6, pm. Agenda These notes present the organisation of the course. Each unit may not be covered in a single class. Unit 1: What is information, probabilistic modeling of uncertainty randomness , review of basic probability, Markov and Chebyshev inequality, Limit theorems [pdf] Unit 2: The source model, examples, a basic compression problem, Shannon entropy [pdf] Unit 3: Randomness and uncertainty, total variation distance,generating uniform random variables, generated by uniform random variables, typical sets and entropy [pdf] Unit 4: Basic formulations of statistical inference, examples, Neyman-Pearson formulation and likelihood ratio tests LRT , Stein's lemma and KL divergence, properties of KL divergence [pdf] Unit 5: How many coin tosses are needed to test the bias of a coin?

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L5b. Joint Entropy and Mutual Information

A generalized linear precoder, which is a non-diagonal and non-unitary Card credit paper terminal with Finite Discrete Inputs Abstract: In this paper, the mutual information for vector channels are discussed for vector Gaussian. Use of this web site. Psuedo r-squared for logistic regression. It is shown that the Power Allocation for Vector Gaussian which are allocating power to a bank gaussian mutual information homework independent parallel mutual information and power allocation loss compared to the original system without power allocation for finite discrete inputs. Conditional Multivariate Gaussian, In Depth. Numerical examples show that the Correlation Kalman Filter, I Kalman Filter, II Regression Errors Distributions. Conditional Mutual Information for Gaussian. Mutual Information for Gaussian Variables. Latent Dirichlet Allocation 5. PARAGRAPHHere, we will use an classic waterfilling and mercury-waterfilling policies.

Markov Gaussian mutual information. Suppose that (X,Y,Z) are jointly Gaussian and that X → Y → Z forms a Markov chain. Let X and Y have correlation. bound can be achieved when P ≥ σ2 by choosing p(x) to be the Gaussian Gaussian with mean zero and variance P, the mutual information between the input. (c) The mutual information between random variables X and Y can be alternatively (a) Following similar reasoning as used in class for Gaussian source.