1 / 21

Digital Communications: Error Correction Coding and Pulse Amplitude Modulation

Learn about error correction coding techniques, including Hamming Code, and the basics of pulse amplitude modulation in digital communications.

djohanna
Download Presentation

Digital Communications: Error Correction Coding and Pulse Amplitude Modulation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related