TAILIEUCHUNG - Information Theory

Statistical communication theory is generally ragarded as having been founed by Shannon( 1948) and Wiene(1949), who conceived of the communication situation as one in which a signal chosen from a specified class is to be tranmitted through of channel, but the output of the channel is not determined by the input | Robert B. Ash INFORMATION THEORY PREFACE Statistical communication theory is generally regarded as having been founded by Shannon 1948 and Wiener 1949 who conceived of the communication situation as one in which a signal chosen from a specified class is to be transmitted through a channel but the output of the channel is not determined by the input. Instead the channel is described statistically by giving a probability distribution over the set of all possible outputs for each permissible input. At the output of the channel a received signal is observed and then a decision is made the objective of the decision being to identify as closely as possible some property of the input signal. The Shannon formulation differs from the Wiener approach in the nature of the transmitted signal and in the type of decision made at the receiver. In the Shannon model a randomly generated message produced by a source of information is encoded that is each possible message that the source can produce is associated with a signal belonging to a specified set. It is the encoded message which is actually transmitted. When the output is received a decoding operation is performed that is a decision is made as to the identity of the particular signal transmitted. The objectives are to increase the size of the vocabulary that is to make the class of inputs as large as possible and at the same time to make the probability of correctly identifying the input signal as large as possible. How well one can do these things depends essentially on the properties of the channel and a fundamental concern is the analysis of different channel models. Another basic problem is the selection of a particular input vocabulary that can be used with a low probability of error. In the Wiener model on the other hand a random signal is to be communicated directly through the channel the encoding step is absent. Furthermore the channel model is essentially fixed. The channel is generally taken to be a device that .

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• statistical
• radar reception
• unique decipherability
• exponential
• minimum distance
• hamming bound
• Statistical techniques
• Statistical techniques in business
• Statistical techniques in economics
• Descriptive statistics
• Statistical inference
• Independent samples
• Statistical process control
• Quality management
• Random observation
• Sampling methods
• Central limit theorem
• Confidence intervals
• Point estimator
• Confidence interval
• Hypothesis testing
• Alternative hypothesis
• Analysis of variance
• F distribution
• Linear regression
• Coefficient of correlation
• Multiple regression
• Multiple regression analysis
• Chi square applications
• Test of hypothesis
• Analysis of ranked data
• Kruskal Wallis test
• Index numbers
• Consumer price index
• Time series
• Linear trend equation
• Decision making
• Organize information
• The role of statistics
• Qualitative variable
• Describing data
• Frequency distribution
• Central tendency
• Standard deviation
• Ungrouped data
• Probability concepts
• Random experiment
• Discrete probability distributions
• Continuous random variables
• Uniform statistical convergence
• Uniform statistical cluster points
• Uniform statistical limit superior
• Asymptotic density
• Summability of subsequences
• Decision theory
• Decision alternative
• Inferential statistics