Digital Communications: Error Correction Coding and Pulse Amplitude Modulation

1. Electrical Communications Systems0909.331.01Spring 2005 Lecture 10aApril 11, 2005 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring05/ecomms/

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

3. ECOMMS: Topics

4. 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

5. 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

6. (7, 4) Hamming Code Code Generator Matrix

7. 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

8. Syndrome Decoding Parity Check Matrix

9. 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

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

11. ECOMMS: Topics

12. 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

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

14. PWM T A Td PTM PAM t Ts Pulse Modulation • Pulse Amplitude Modulation (PAM): A m(t) • Pulse Time Modulation (PTM): Td m(t) • Pulse Width Modulation (PWM): T m(t)

15. 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

16. 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

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

19. 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

20. 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

21. Summary