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# Understanding Channel Coding and Capacity in Information Theory

## Learn about the significance of codes in transmitting information reliably with this free online course.

Publisher: NPTEL
Have you ever wondered what happens during the communication process between two mediums? This course aims to answer this question by illustrating the process of digital communication channels. You will be taught about the procedure for safeguarding the information against noises during transmission. Study the methods of determining the rate of information transmission in a communication channel by enrolling in this course now.

5-6 Hours

13

CPD

## Description

The fundamentals of channel coding and channel capacity are the core components of this course. It begins with explaining the importance of channel codes in information theory. You will discover how these coding schemes look after the data from being tainted in the communication channel. This will include the method of conveying accurate information in a noise-degraded communication channel. Next, you will study the concepts of ‘mapping’ and ‘inverse mapping’ of the input-output data sequences. You will comprehend the role of transmitters and decoders in the mapping process for eliminating channel noise. Following this, the proof of Shannon’s channel coding theorem for the binary symmetric channel is explained. You will discover the implication of sphere-packing bound in allowing the error-amending codes to utilize the embedded code words. The process of restraining the factors of a random block code is described. The course explores the core parameters required for a code to be deemed perfect in terms of its representation.

Next, the course explains the procedure for resolving the inaccuracy for a given code using the random coding bound method. You will explore how the bound is established based on the mean probability error over a collection of codes. In addition to this, the significance of random coding in demonstrating the parts of achievability in the network information theory is explained. Next, the processes of extending the proof of the Shannon coding theorem for other general channels are explored. You will discover the importance of strong and weak converse in transmitting error-correcting codes to various communication channels. Following this, the concept of utilizing the Gaussian channels in channel capacity is highlighted. You will explore the extension process of these channels to an uninterrupted signal channel with a measure of various bandwidths. In addition to this, you will explore the methods of associating transmission systems with Shannon limits. The roles of time-discrete channels in modelling other communication channels are also described.

Finally, the course illustrates the process of deriving the channel coding theorem in the Gaussian channel. You will explore the converse and achievability proofs of the theorem. Next, you will explore the various kinds of parallel channels used in the channel capacity. The notions of orthogonal frequency-division multiplexing (OFDM), multiple-input-multiple-output (MIMO) and discrete multi-tone systems (DSL) are clarified. In addition to this, you will comprehend the significance of the parallel independent channels in increasing the total capacity by dispensing power across various channels. Lastly, you will study the need for performing equalization approaches on communication channels. You will discover the implications of water-filling algorithms in enhancing the number of data rates in all sub-channels by assigning maximum power with a healthier signal to noise ratio (SNR). ‘Understanding Channel Coding and Capacity in Information Theory’ is an enlightening course that explores the basics of coding for dependable transmission over noisy channels. Start learning about the process of communicating precise information with minimum probability of error.

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