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Unformatted text preview: E4702: Communication Theory Lecture Outline Course Logistics S y l l a b u s Lecture 1: Probability & Random Variables Course Information: People Instructors: Angel Lozano ( aloz@lucent.com ) & Rob Soni ( rsoni@lucent.com ). OHs: Wd 2:004:00 and by appointment, MUDD 1312 . TA: Ali Tajer. OHs: 713 CEPSR, Tu 3:304:30. Course Information Prerequisites: E3701 or equivalent (communication signal & systems). Notions of probability and random variables (although we will review that today). Textbook: Communication Systems Engineering (by J. Proakis and M. Salehi). Either 1 st (1994) or 2 nd (2002) editions acceptable, although careful with chapter numbering. Class Homepage: All announcements, homeworks, etc, will be posted. One weekly session (with a break). Credit: 3 units towards any degree. Grading: HWs 20%, Midterm and Final Exams 30%, 50%. HWs: assigned Wd on/after lecture, due week after (before lecture). CVN students follow CVN procedures. Exams: Midterm Exam on Oct. 24 th. Final Exam on Dec 19 th . Course Policies Goal Solid understanding of the techniques that are essential to the operation of a digital communication system. Course Syllabus Introduction Review of Probability & Random Variables Source Coding Channel Coding Digital Transmission over AWGN Channels Basic Digital Modulation Systems Digital Transmission over Bandlimited Channels Wireless Communications (Time Permitting) Lecture 1: Probability & Random Variables Lecture Outline M o t i v a t i o n Probability Conditional probability Random Variables (R.V.s) Discrete Continuous Random Vectors Expectations & Moments Transformations of a R.V. R a n d o m p r o c e s s e s Representing Rations & Powers Motivation Why are probability and r.v.s relevant to communication theory ? Most events and phenomena in a communication system can be accurately modeled using r.v.s. Their behavior is then well described by the tools of probability theory. Signals Noise and interference Channel behaviors (attenuation, phase rotation, delay, etc). User behavior etc Definitions Consider an experiment, such as a coin toss, that can be repeated arbitrarily often. Outcome ( w ): Result of the experiment. Sample space ( ): Set of all possible outcomes. Events (A, B, C, etc): Subsets of sample space. Example: Coin tossed 3 times in succession. Sample space is ={ w 1 , w 2 , w 3 , w 4 , w 5 , w 6 , w 7 , w 8 } given w 1 w 2 w 3 w 4 w 5 w 6 w 7 w 8 HHH HHT HTH THH HTT THT TTH TTT Event: First toss is H = { w 1 , w 2 , w 3 , w 5 }....
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This note was uploaded on 08/05/2008 for the course ELEN E4703 taught by Professor Lazano during the Summer '08 term at Columbia.
 Summer '08
 LAZANO

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