ECE 4371, Fall, 2013 Introduction to Telecommunication Engineering/Telecommunication Laboratory

1. ECE 4371, Fall, 2013Introduction to Telecommunication Engineering/Telecommunication Laboratory Zhu Han Department of Electrical and Computer Engineering Class 17 Oct. 30th, 2013

2. Outline • Quick Review of last class • Line Code, Hamming code • 4117 • S352, access should be ok after 1 month • Call me or go to W319 if you cannot enter • USRP2 lab 1 due 11/25. • Lab 2 due at the final exam • Term Project

3. ARQ • Acknowledgments from receiver • Positive: “okay” or “ACK” • Negative: “please repeat that” or “NACK” • Timeout by the sender (“stop and wait”) • Don’t wait indefinitely without receiving some response • … whether a positive or a negative acknowledgment • Retransmission by the sender • After receiving a “NACK” from the receiver • After receiving no feedback from the receiver

4. Types of Error Correcting Codes • Repetition Code • Linear Block Code, e.g. Hamming • Cyclic Code, e.g. CRC • BCH and RS Code • Convolutional Code • Tradition, Viterbi Decoding • Turbo Code • LDPC Code • Coded Modulation • TCM • BICM

5. Hamming Code • H(n,k): k information bit length, n overall code length • n=2^m-1, k=2^m-m-1: • H(7,4), rate (4/7); H(15,11), rate (11/15); H(31,26), rate (26/31) • H(7,4): Distance d=3, correction ability 1, detection ability 2. • Remember that it is good to have larger distance and rate. • Larger n means larger delay, but usually better code

6. Hamming Code Example • H(7,4) • Generator matrix G: first 4-by-4 identical matrix • Message information vector p • Transmission vector x • Received vector r and error vector e • Parity check matrix H

7. Error Correction • If there is no error, syndrome vector z=zeros • If there is one error at location 2 • New syndrome vector z is which corresponds to the second column of H. Thus, an error has been detected in position 2, and can be corrected

8. Exercise • Same problem as the previous slide, but p=(1001)’ and the error occurs at location 4 instead. • Pause for 5 minutes • Might be 4 points in the finals.

9. Important Hamming Codes • Hamming (7,4,3)-code. It has 16 codewords of length 7. It can be used to send 27=128 messages and can be used to correct1 error. • Golay (23,12,7) -code. It has 4 096 codewords. It can be usedto transmit 8 3888 608 messages and can correct 3 errors. • Quadratic residue (47,24,11)-code. It has16 777 216codewords and can be used to transmit 140 737 488 355 238messages and correct 5 errors.

10. Another Example: Encoding To encode our message But why? we multiply this matrix You can verify that: Hamming[1 0 0 0]=[1 0 0 0 0 1 1] Hamming[0 1 0 0]=[0 1 0 0 1 0 1] Hamming[0 0 1 0]=[0 0 1 0 1 1 0] Hamming[0 0 0 1]=[0 0 0 1 1 1 1] By our message Where multiplication is the logical AND And addition is the logical XOR

11. Example: Add noise • If our message is Message = [0 1 1 0] • Our Multiplying yields Code = [0 1 1 0 0 1 1] Lets add an error, so Pick a digit to mutate Code => [0 1 0 0 0 1 1]

12. Example: Testing the message The matrix used to decode is: To test if a code is valid: • Does Decoder*CodeT =[0 0 0] • Yes means its valid • No means it has error/s • We receive the erroneous string: Code = [0 1 0 0 0 1 1] • We test it: Decoder*CodeT =[0 1 1] • And indeed it has an error

13. Example: Repairing the message • To repair the code we find the collumn in the decoder matrix whose elements are the row results of the test vector • We then change • We trim our received code by 3 elements and we have our original message. [0 1 1 0 0 1 1] => [0 1 1 0] • Decoder*codeT is [ 0 1 1] • This is the third element of our code • Our repaired code is [0 1 1 0 0 1 1]

14. Coding Gain • Coding Rate R=k/n, k, no. of message symbol, n overall symbol • Word SNR and bit SNR • For a coding scheme, the coding gain at a given bit error probability is defined as the difference between the energy per information bit required by the coding scheme to achieve the given bit error probability and that by uncoded transmission.

15. Coding Gain Example ECE 4371 Fall 2008

16. Encoder/Decoder of Linear Code • Encoder: just xor gates • Decoder: Syndrome

17. Reed–Muller code

18. Technical Writing • Structure, Logic (between sentences and paragraphs), and Strictness (no holes). • Know who is your audiences • Structure • Title and keyword: concise and hit the point, for google users • Abstract: 200 words, for directors who have 20 seconds • Why it is a good topic • What is the idea and contribution • What are the results • Introduction: 2 to 3 pages, for managers who have 5 minutes • Why it is a good topic • What are in the literature, or what are the competitors • What is the idea and contribution • What are the results • (Organization) • System model • Problem formulation, proposed scheme, and analysis • Results • Conclusions • Citations For peer

19. Term Project, Choice One • Due at last regular class so that I can talk about it during additional class. • Goal: If you have interview on company for wireless project xxx, what you should know • Source • The company listed on the web or some company you know. • Select the cool project interesting you. Send me an email by 11/16 • Structure • Abstract: 100 words for the company, the project and why interests • Introduction: 1 pages for the company: history, competitors, project lines, future, stocks, etc. • Main body of 3 pages for a specific product: 2 pages for the thing you have studied from this class, 1 page for something new.

20. Term Project, Choice two • What is the state of art of xxx • Bluetooth, UWB, WLAN, WMAN, 3G, Ad hoc/Sensor Networks Cognitive Radio, Fiber communication, Cable communication, Power line communication, Satellite communication, etc. • Source • IEEE communication magazine to get some tutorial papers • Important citations can be found by IEEE Xplore • Citeseer to test if the paper is well cited and recognized • Select a topic by 11/11. • Writing • Goal: suppose you were me and want to give a lecture on the state of art of xxx. • 200 words abstract, 1 page introduction and 3 pages details, excluding the figures. • Citations are needed if you “copy” some ideas.