Electrical Communications Systems ECE.09.331 Spring 2008

1. Electrical Communications SystemsECE.09.331Spring 2008 Lecture 11aApril 8, 2008 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring08/ecomms/

2. Plan • Digital Baseband Communications • Error Control Coding • Hamming Distance • Error Detection Coding • Parity Check Code • Error Correction Coding • Hamming Code • Pulse Amplitude Modulation • Sampling • Quantization • TDM Standards • T1 (DS-1) Line • North American TDMA Hierarchy

3. ECOMMS: Topics

4. Digital Communications Transceiver Anti- aliasing Filter Error Control Encoder Data Encryption Encoder Channel/ Line Encoder Source Encoder Sampling Quantization Modulator MUX ADC Analog i/p CODEC MODEM Multiple access channel Analog o/p Error Control Decoder Data Encryption Decoder Source Decoder Audio Amp Reconstruction/ DAC Equalization / Decision Circuits Demod-ulator DEMUX

5. Error Control Coding Error Detection (ARQ Technique) Error Correction (FEC Technique) • Hamming Distance The number of locations (bits) at which two code words differ • Theorem 1 A code with a Hamming distance of d >= t+1 can detect t errors in the received code word • Theorem 2 A code with a Hamming distance of 2t+1 <= d <= 2t+2 can detect and correct t errors in the received code word

6. Block Coder n encoded bits k information bits k n-k Information bits Parity bits Add Redundancy!! n-bit codeword Error Control Codes Block Codes (memoryless) Convolutional Codes (with memory) Principle Will not discuss! (n, k) systematic block code

7. I6 I4 I7 I5 I3 I2 I1 P Parity Check Codes P is set such that the total no. of bits in the code word is even or odd

8. 1 Rx 2 3 3 NACK ACK ACK 1 2 3 Tx Error detected!!! Remediation for Detected Errors: ARQ

9. I3 I1 I4 I2 P3 P2 P1 (7, 4) Hamming Code • Single error detection and correction code • Hamming distance, d = 3 • Fits into a general category of coding techniques called BCH codes • Employs a • Code Generator Matrix • Syndrome Decoding Technique

10. I3 I3 I1 I1 I4 I4 I2 I2 P3 s3 s2 P2 P1 s1 R6 C6 R4 C4 C7 R7 C5 R5 C3 R3 C2 R2 R1 C1 (7, 4) Hamming Code Encoding Parity bits Code Generator = Info bits Code word Decoding Parity Check Received code word Error position indicator

11. (7, 4) Hamming Code Code Generator Matrix

12. I3 I1 I4 I2 P3 P2 P1 + + + Hamming Encoder Info bits Parity bits P3 = I4 I2 I1 P2 = I4 I3 I1 P1 = I4 I3 I2

13. Syndrome Decoding Parity Check Matrix

14. s3 s2 s1 R6 R4 R7 R5 R3 R2 R1 Hamming Decoder Received code word Error Position Indicator + + + s3 = R7 R5 R4  R3 s2 = R7 R6 R4  R2 s1 = R7 R6 R5  R1

15. Hamming Decoder Error position indicator (syndrome) s Error Position, e No error

16. ECOMMS: Topics

17. Digital Communications Transceiver Anti- aliasing Filter Error Control Encoder Data Encryption Encoder Channel/ Line Encoder Source Encoder Sampling Quantization Modulator MUX ADC Analog i/p CODEC MODEM Multiple access channel Analog o/p Error Control Decoder Data Encryption Decoder Source Decoder Audio Amp Reconstruction/ DAC Equalization / Decision Circuits Demod-ulator DEMUX

18. Pulse Code Modulation (PCM) • Standard for all digital communications Analog Signal Sample & Hold Digital Bitstream Quantize Encode PAM PCM

19. 8 Analog PAM 6 4 2 0 -2 -4 -6 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 time Pulse Amplitude Modulation: Flat-top Sampling Matlab Demo: pam.m

20. Quantization Uniform Non-Uniform m-Law A-Law Mid-rise Mid-tread Matlab Demos: quantization.m pcm.m • Mid-rise • Mid-tread • Mid-rise • Mid-tread Matlab Demos: companding.m pcm_mucompand.m pcm_mucompand2.m pcm_acompand.m pcm_acompand2.m

21. Digital Communications Transceiver Anti- aliasing Filter Error Control Encoder Data Encryption Encoder Channel/ Line Encoder Source Encoder Sampling Quantization Modulator MUX ADC Analog i/p CODEC MODEM Multiple access channel Analog o/p Error Control Decoder Data Encryption Decoder Source Decoder Audio Amp Reconstruction/ DAC Equalization / Decision Circuits Demod-ulator DEMUX

22. Decode Time Division Multiplexing Message 1 Quantize & Encode Message 2 Channel Message N Message 1 LPF Message 2 LPF Message N LPF

23. Channel 1 Channel 24 Channel 2 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 T1-Line TDM Format 1 Frame = (24 Channels + F) = 125 ms F 193 bits Frame Sync Bit Even Frames: 0 0 1 1 1 0 Odd Frames: 1 0 1 0 1 0 Every Sixth Frame LSB (8th bit) is a Signaling bit Bipolar R-Z Line Encoding

24. 24 6 1 7 1 1 1 2 4 1 5th M U X 3rd M U X 2nd M U X 4th M U X DS-2 6.312 Mbs 96 VF DS-3 44.736 Mbs 672 VF DS-4 274.176 Mbs 4032 VF DS-1 1.44 Mbs 24 VF North American TDMA Hierarchy 64 kbs 1 VF DS-0 1st M U X DS-5 560.160 Mbs 8064 VF • Figure 3-40, p. 207 in Couch • Table 3-8, p. 208 in Couch • Table 3-9, p. 209 in Couch

25. Summary