An AWGN Multiaccess Channel Ballard Blair 6 441
An AWGN Multiaccess Channel* Ballard Blair 6. 441 - Transmission of Information Massachusetts Institute of Technology May 10, 2007 5/10/2007 *Paper: Gallager, R, A Perspective on Multiaccess Channels, IEEE transactions on Information Theory, March AWGN Multiaccess channel - Ballard Blair 1985
Motivation T 1 T 2 T 3 TN Channel R Multiaccess Network • Generalization of point to point • Transmitter not always ready • Applicable to many situations – Cell phones – Ethernet • Encoding Easy (Random), Decoding Hard • Conclusion: Need better models and approaches 5/10/2007 AWGN Multiaccess channel - Ballard Blair 2
AWGN Channel Setup T 1 T 2 Coding x y=w+x+z w R Coding z Gaussian Multiaccess Setup Types of Errors – Only X decoded incorrectly (type 1) – Only Y decoded incorrectly (type 2) – X and Y decoded incorrectly (type 3) Capacity of AWGN Channel: • 5/10/2007 Energy Constraint for each transmitter (S 1 and S 2) AWGN Multiaccess channel - Ballard Blair 3
Achievable Rates R 2 I(W; Y|X) I(W; Y) I(X; Y|W) R 1 Constraints 2 -Parallel AWGN Channels 5/10/2007 AWGN Multiaccess channel - Ballard Blair 4
Higher Dimensionality R 3 R 1 R 2 3 Transmitters (7 constraints) Constraints quickly get out of hand (2 n-1 constraints for n-dim) 5/10/2007 AWGN Multiaccess channel - Ballard Blair 5
Conclusions • AWGN Multiaccess – Interesting, not practical – Better Models needed (other than power lim) • Modern Approaches – CDMA – OFDM 5/10/2007 AWGN Multiaccess channel - Ballard Blair 6
Questions? http: //www. ukuleleman. net/2005_08_01_ukemanspeaks_archive. html 5/10/2007 AWGN Multiaccess channel - Ballard Blair 7
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