AbstractIn a digital link, a transmitter converts bits into signals and a receiver converts the signals it receives into bits. The receiver faces a decision problem that we study in Sect. 7.1. The main tool is Bayes’ Rule. The key notions are maximum a posteriori and maximum likelihood estimates. Transmission systems use codes to reduce the number of bits they need to transmit. Section 7.2 explains the Huffman codes that minimize the expected number of bits needed to transmit symbols; the idea is to use fewer bits for more likely symbols. Section 7.3 explores a commonly used model of a communication channel: the binary symmetric channel. It explains how to calculate the probability of errors. Section 7.4 studies a more complex modulation scheme employed by most smartphones and computers: QAM. Section 7.5 is devoted to a central problem in decision making: how to infer which situation is in force from observations. Does a test reveal the presence of a disease; how to balance the probability of false positive and that of false negative? The main result of that section is the Neyman–Pearson Theorem that the section illustrates with many examples.
Effect of a Binary Symmetric Channel on the Synchronisation Recovery of Variable Length Codes
