lecture1 - ECE 5670 : Digital Communications Lecture 1:...

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ECE 5670 : Digital Communications Lecture 1: Discrete Nature of information 1 1/25/2011 Instructor: Salman Avestimehr 1 Introduction The currency of today’s information age is digital: bits . Digital communication is reliable transmission of this currency over an unreliable physical medium. It is an interesting ques- tion to ask why very diFerent types of information sources such as voice and video are represented using a common currency, but we will not pursue this question in this course. It is quite a loaded question and the ±nal word on the matter is not yet said; answers to this question in certain communication contexts are provided in a separate ±eld of study known as information theory. The block diagram in ²igure 1 shows a high level representation of a typical communication system. The discrete message source continuously outputs a stream of bits that represent the information we would like to transmit. Bits are abstract entities that need to be mapped to a physical quantity, such as an electromagnetic signal, to be transmitted over a physical medium. Message Source - Transmitter - Channel ? Distortion - Receiver ²igure 1: The basic block diagram of a communication system The behavior of the physical medium is uncertain: what you get is not a deterministic function of what you send; this uncertainty is the essence of communication. While the behavior of the channel 2 over one experiment cannot be predicted, the average behavior, averaged over many experiments, turns out to be well behaved in many physically interesting scenarios. The characterization of the average behavior, or in other words, the statistical characterization of the physical medium is crucial to understanding how to communicate the bits reliably to the receiver. A primary component of the communication engineer’s tool-box is a robust and reasonable statistical model of important physical channels such as the wireline telephone channel and the wireless channels. 1 Based on lecture notes of Professor Pramod Viswanath at UIUC. 2 Channel is a term we will use throughout these notes to denote the unreliable physical medium. 1
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2 A Deterministic Additive Noise Model We will begin with a simple form of a physical medium where we only transmit and receive voltages (real numbers). The received voltage y , is the transmitted voltage x , plus “noise” w : y = x + w (1) The simplest model of the noise is that w is strictly within a certain range, say ± σ .Ino the r words, we receive a voltage that is within ± σ Volts from the voltage we transmitted. 2.1 A Simple Communication Scheme Suppose we want to send a single bit across this channel. We can do this by transmitting a voltage v 0 to communicate an information content of the bit being “zero”, and a voltage v 1 when transmitting an information content of the bit being “one”. As long as | v 0 v 1 | > 2 σ, (2) we can be certain that our communication of the one bit of information is reliable over this channel. Physically, the voltage transmitted corresponds to some energy being spent: we
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lecture1 - ECE 5670 : Digital Communications Lecture 1:...

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