To achieve a better understanding of digital communications, some basic principles of probability theory need to be discussed. This chapter provides an overview of theory necessary for the design of digital communications and spread spectrum systems. Probability is used to calculate the link budget in regard to the error and required signal-to-noise ratio (SNR) and to determine whether a transceiver is going to work and at what distances. This is specified for digital communications systems as the required E_b/N_o.

Chapter Contents:

• 6.1 Basic probability concepts
• 6.2 The Gaussian process
• 6.3 Quantization and sampling errors
• 6.4 Probability of error
• 6.5 Error detection and correction
• 6.5.1 Error detection
• 6.5.2 Error detection using parity
• 6.5.3 Error detection using checksum
• 6.5.4 Error detection using CRC
• 6.5.5 Error correction
• 6.5.6 Error correction using redundancy
• 6.5.7 Forward error correction
• 6.5.8 Types of FEC
• 6.5.9 Interleaving
• 6.5.10 Viterbi decoder
• 6.5.11 Turbo and low-density parity check codes
• 6.6 Theory of pulse systems
• 6.7 PN code
• 6.8 Summary
• 6.9 Problems
• Further reading

Inspec keywords: digital communication; probability; spread spectrum communication

Other keywords: link budget; spread spectrum systems; digital communications systems; signal-to-noise ratio; transceiver; probability theory; pulse theory; SNR

Subjects: Other topics in statistics; Radio links and equipment