Basic Probability and Pulse Theory

Basic Probability and Pulse Theory

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A simple approach to understanding probability theory and the Gaussian process is provided to allow the designer to better understand the principles of designing and evaluating digital transmission. Quantization and sampling errors in the analysis and design of digital systems were discussed. The probability of error, probability of detection, and probability of false alarms are the keys in determining the performance of the receiver. These errors are dependent on the received SNR and the type of modulation used. Error detection and correction were discussed and several approaches were examined to mitigate errors. Theory on pulsed systems, showing time and frequency domain plots, provide knowledge and insight into the design and optimization of digital transceivers.

Chapter Contents:

  • 6.1 The Gaussian Process
  • 6.2 Quantization and Sampling Errors
  • 6.3 Probability of Error
  • 6.4 Probability of Detection and False Alarms
  • 6.5 Pulsed System Probabilities Using the BDF
  • 6.6 Error Detection and Correction
  • 6.6.1 Error Detection
  • 6.6.2 Error Detection Using Parity
  • 6.6.3 Error Detection Using Checksum
  • 6.6.4 Error Detection Using CRC
  • 6.6.5 Error Correction
  • 6.6.6 Error Correction using Redundancy
  • 6.6.7 Forward Error Correction
  • 6.6.8 Interleaving
  • 6.6.9 Types of FEC
  • 6.6.10 Block Codes
  • 6.6.11 Linear Block Codes
  • 6.6.12 Hamming Code
  • 6.6.13 Convolutional Codes
  • 6.7 Viterbi Decoder
  • 6.7.1 Multi-h
  • 6.8 Turbo and Low-Density Parity Check Codes
  • 6.9 Theory of Pulse Systems
  • 6.10 PN Code
  • 6.11 Summary

Inspec keywords: error detection; error correction; time-domain analysis; error statistics; frequency-domain analysis; quantisation (signal); radio transceivers; Gaussian processes; optimisation

Other keywords: pulse theory; time domain plots; modulation; sampling errors; digital systems; basic probability; false alarms; frequency domain plots; digital transceivers; error probability; Gaussian process; receiver; optimization; error correction; digital transmission; error detection; quantization; received SNR

Subjects: Signal processing and detection; Radio links and equipment; Mathematical analysis; Optimisation techniques; Other topics in statistics

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