6.441-15 Joint source channel coding
LECTURE 15Last time:Feedback channel: setting up the prob₭ lem Perfect feedback • Feedback capacity • Lecture outlineData compression • Joint source and channel coding theorem • Converse • Robustness • Brain teaser • Reading: Sct. 8.13. Data compressionConsider coding several symbols togetherC : X n �→ D∗ expected codeword length is �xn∈X n PXn(xn)l(xn) optimum satisfies HD(Xn) ≤ L∗≤ HD(Xn)+1 per symbol codeword length is HD(Xn) n ≤ L∗ n ≤ HD(Xn) n + 1 n Thus, we have that the rate R is lower bounded by entropy Channel codingCoding theorem: For any source of messages, any rate R below C is feasible, i.e achievable with low enough probability of error Ecodebooks,messages[Pe] ≤ 2−NEr(R,PX ) For the PX that yields capacity, Er(R, PX) is positive for R
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Lecture outline: Data compression,Joint source and channel coding theorem,Converse,Robustness,Brain teaser. Coding theorem:For any source of messages, any rate R below C is feasible, i.e achievable with low enough probability of error. Here we discuss about should coding be done jointly or not?Moreover, the source coding and the channel coding may be done independently.The joint channel source coding theorem and its converse hold under very general conditions:memory in the input memory, in channel state and multiple access
Instructors: Prof. Muriel Médard, MIT Course Number:6.441 Level: Graduate, 6.441-15 Joint source channel coding, 6.441 Information Theory, Electrical Engineering and Computer Science, Engineering, Massachusetts Institute of Technology: MIT Open Course Ware, http://ocw.mit.edu (11-09-2011).License: Creative Commons BY-NC-SA: http://ocw.mit.edu/terms/#cc".
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