Module6_1 - Module 6, Lecture 1 Channel Coding:...

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Module 6, Lecture 1 Channel Coding: Introduction G.L. Heileman Module 6, Lecture 1
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Channel Coding Introduction In the last module, we assumed the channel from the source encoder to the source decoder was error free. In this module we consider how to deal with the situation of when the channel is not error free. Specifically, we will investigate the fundamental possibilities and limitations of error-free communication over a noisy channel. These possibilities and limitations will be expressed in the important Noisy Channel Coding Theorem due to Shannon. G.L. Heileman Module 6, Lecture 1
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Channel Coding Introduction Big Picture – message source message destination source encoder channel encoder encryption decryption noisy channel modulator/ demodulator transmitter receiver/ { } X n Y n { } S ( ) t source decoder channel decoder amplitude/ phase change signal distortion noise S ( ) t N ( ) t + R ( ) t = p( ) ( ) y|x W W We will characterize a noisy channel using p ( y | x ). G.L. Heileman Module 6, Lecture 1
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Channel Models Examples of noisy communication channels: Radio communication between the Cassini spacecraft (visiting Saturn) and the earth (a distance of over one billion miles). The radio signals are corrupted by background radiation from terrestrial and cosmic sources. Analog phone line, over which a pair of digital modems are communicating. Noise is commonly introduced during transmission, e.g., impulse noise due to lightening, noisy electromechanical equipment, crosstalk from an adjacent channel, etc. G.L. Heileman Module 6, Lecture 1
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Channel Models Examples of noisy communication channels: Disk drive. A bit is stored by aligning a patch of magnetic material in one of two orientations. Numerous things (e.g., junior’s magnet) can cause the patch to flip orientation, or the R/W head could receive a burst of thermal noise causing the circuitry to read the wrong value. This example does not involve the transfer of information from one place to another – the separation is temporal, as we’d like to read the bit at a later point in time. Digital Watermarking. Involves embedding information, below the perceptual threshold, in digital content (e.g., music, images, movies, etc.). The content is the channel, and the hidden information is the message. An attacher, intent on removing the information, manipulates the content, and this is the noise. G.L. Heileman Module 6, Lecture 1
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Channel Models In all of the examples just described, there is some probability that the received signal will not be identical to the transmitted one.
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Module6_1 - Module 6, Lecture 1 Channel Coding:...

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