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UNIT 7 INFORMATION THEORY ————————————————————————————— ———— Structure

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UNIT 7 INFORMATION THEORY ————————————————————————————— ———— Structure ————————————————————————————— ———— UNIT 7 INFORMATION THEORY ————————————————————————————— ———— Structure 7.0 Objectives 7.1 Introduction 7.2 Approaches to Information Theory 7.3 Information Basics 7.4 Information Measure 7.5 Information Entropy 7.6 Information Communication 7.6.1 Efficient Communication 7.6.2 Reliable Communication 7.7 Semantic Information Theory 7.8 Summary 7.9 Answers to Self-Check Exercises 7.10 Keywords 7.11 References and Further Reading ————————————————————————————— ———— 7.0 OBJECTIVES ————————————————————————————— ———— After reading this Unit, you will be able to understand and appreciate: • importance of information in the present-day society • recognise the need for information theory • different perspectives of information • different approaches to information theory • a scientific definition of information • information as part of human thought process • how to measure information • what is information entropy • how to calculate information entropy • how to achieve efficiency in information transfer • what is source coding and its purpose • channel coding for reliable information transfer • basics of semantic information theory • relative information content measures • different parameters that define the context ————————————————————————————— ———— 7.1 INTRODUCTION ————————————————————————————— ———— Quest for knowledge has been a central theme of human evolution. Information is a key component in the growth of knowledge. From early civilisation of mankind, information has played a significant role in societal development and in improving living standards of human beings. Information is closely linked with the growth of economic, political, 1 health, cultural, educational and other sectors of a nation. It is now well recognised that effective use of information can turn hitherto non- productive resources into value added economic resources. Good examples of this are biogas and fuel pellets made out of human waste. Information contributes to political strength of countries so much, that we talk of information-rich nations being more powerful than information- poor nations. Successful application of science and technology (S&T) to social and economic developments depends on the effective use of information. Many countries have set up special purpose S&T information centres accessible to common man. India has over a dozen such centres. The increase in life expectancy and the growing population have resulted in large-scale governmental operations that call for extensive use of information. Thus, at present times, information has come to occupy a central role in national development and is reckoned as a driving force for all human activities. Consequently, the present society is termed as information society. Information is useful only when communicated from originators to other potential users of information. Information communication is as ancient as information itself. In the early days, messengers used to carry information from one person to another. Birds were trained to carry messages. There were other techniques that used free space as the communication medium. Beating drums, waving flags and lighting fires are some of these ancient techniques. Inherent in these techniques is the concept of coding where a particular action conveyed a certain predetermined message. For example, waving a red flag may be a warning of an impending danger. The next major step in information communication is the postal network that is used quite extensively today. Modern telecommunications started with telegraphy in 1837. These systems transport information via electrical, optical or electromagnetic signals. Until about 1950s, the telecommunication systems were based on analog technology. Principles of digital communication were propounded in the second half of 1930s and first digital computers were built in mid 1940s. Since then, the digital technology has been advancing leaps and bounds both in the fields of communications and computers. Binary coding is used extensively in these systems. Yet another aspect of information that needs attention is its enormous volume. In the early days of human civilisation, information generation was a slow process. The population was small and only a few individuals were involved in the process of creating new knowledge. The advent of industrial age accompanied by an increase in world population has brought about significant growth in information generation and dissemination. By the year 1800, the quantum of information generated was doubling every 50 years and by the year 1950, it was doubling every 10 years. The quantum of information generated by industry, governments and the academic world reached unmanageable proportions by the middle of 20th century that a need was felt to devise new ways for managing information. A search in this direction has given birth to the new information technology (IT). The amount of information generated by the academic community is gauged by the fact that there are around 150,000 journals and periodicals being published at present in the fields of science, engineering, technology, medicine, social sciences, arts and humanities. This means that on an average 15 million articles are written by the academic community every year. Industry is no different. It is said that the weight of 2 the drawings of a jet plane is greater than the weight of the jet plane itself. Remote sensing satellites gather terabytes (1012 bytes) of information everyday, which is equivalent to a million books of about 300 pages each. The banking and finance industry has a large volume of financial and personnel information stored in its vast data banks. The quantum of Government information is mind-boggling too. Land records, population records, voter lists, police records, licensing records, transaction records, accounting records, policies, rules, regulations, laws, judgements and other innumerable pieces of information are ever growing. Thus, information has become the central theme of living these days. It is treated as a commodity and traded for a price. Information economics has emerged as a subject of recent interest. The world is witnessing a phenomenon of information explosion. Consequently, the present period of human civilisation is aptly called the information age. Historically, the information age is supposed to have set in since early 1970s and is expected to last for another century or two. In the context of information society and information age, a number of questions related to information have arisen. What constitutes information? How can we transmit information reliably and efficiently using modern telecommunication systems? How can we store large volumes of information in a compact form? Is there a measure for information? Can we evaluate the information content by attaching value to information? Such questions have led to the development of information theory that deals with the following aspects: • Concept of information • Information measure • Information content • Information communication • Information storage This Unit is a study of the various aspects of information theory. ————————————————————————————— ———— 7.2 APPROACHES TO INFORMATION THEORY ————————————————————————————— ———— Studies in information theory have been pursued using three different perspectives of information: • Syntactic perspective • Semantic perspective • Contextual perspective Studies using syntactic perspective concentrate on the source characteristics and its symbol set usage. These studies do not concern themselves with the semantic aspects of information. Their primary focus is on how to represent and communicate information effectively and reliably via the modern communication systems. They view information as something conveyed by messages put out by the source. The messages are constructed using the symbol set of the source. They measure the information content of messages by analysing the occurrences of the constituent symbols. Consider the following two sentences: 1. Dr. Jaideep Sharma is co-ordinating the preparation of this Unit. 3 2. The preparation of this Unit is being co-ordinated by Dr. Jaideep Sharma. The two sentences are syntactically different but convey the same meaning. A syntactic analysis may yield different values for the information content of the two sentences. The values may, however, differ only marginally. A syntactic technique may code the two sentences in different ways to achieve efficiency in transmission. For example, let us consider some form of binary coding and a binary transmission channel. If it is known that the first syntactic form is used more often, then it can be coded as a smaller binary string and the second one as a larger string. Such coding would, on an average, result in less number of bits being transmitted on the channel and in the consequent efficient utilisation of the channel. Semantic perspective is concerned with complete and precise meaning of the messages as well as relative information content between messages. Contextual perspective of information derives the meaning of messages from not only what is contained in the message but also from the context in which the message occurs. Contextual perspective is also known as pragmatic perspective of information. Consider the following three messages pertaining to the same situation: 1. There is a traffic jam on the National Highway No. 3 (NH 3) between New Delhi and Agra in India. Time: 11:30 Hours. Date: 2 April 2005. 2. There is traffic jam on this highway. 3. There is traffic
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