Digital Communication Playlist: Basics of Block Code

Introduction

• Instructor: Professor Hitesh Dhodakia
• Overview of sessions focusing on block code in digital communication.
• Future sessions will cover different types of block code.

Session Outline

1. Basics of channel and code word
2. Structure of communication system
3. Need for channel encoding via block code
4. Important parameters regarding block code
5. Example of 4,3 block code
6. Representation of block code

Basics of Channel and Code Word

• Channel Limits: Every channel (optical fiber, wireless, coaxial) has an upper limit on the transmission rate (channel capacity).
• Channel Capacity: The limitation on the capacity of a channel to transmit information reliably.
• Error Introduction: Noise in the channel may cause errors in received signals.
• Error Correction: To ensure reliable data, errors must be corrected using block code.

What is Block Code?

• A block code is a set of words with a specific mathematical structure, consisting of a fixed number of bits (codewords).
• Codeword: A sequence of bits sent as signals, capable of correcting errors up to a certain extent.

Structure of Communication System

• Transmitter:
  • Source Encoder
  • Channel Encoder
  • Modulator
• Receiver:
  • Demodulator
  • Channel Decoder
  • Source Decoder
• Channel Encoding: Block code is added at the channel encoder to resolve errors.
• Source Encoding: Reduces redundancy for better bandwidth utilization but does not correct errors.

Basics of Block Code

• Information Bits (K): Represented as I1, I2, ..., IK
• Total Bits (N): N = K + R (R is the number of parity bits)
• Block Code Representation: Notation used is (n, k), where
  • n = total number of bits
  • k = information bits
  • R = n - k
• Codeword Types:
  • Systematic Codeword: Information bits are grouped together.
  • Non-Systematic Codeword: Information bits are not grouped together (random arrangement).

Important Parameters of Block Code

• Total codewords based on block code:
  • 2^n (for total bits)
  • 2^k (for information bits)
  • Redundant codewords: 2^(n - k)
• Code Rate: r = k/n (where k is the information bit and n is total bits).

Example of 4,3 Block Code

• 4,3 Block Code:
  • Total bits = 4
  • Information bits = 3
  • Parity bits = 1 (4 - 3 = 1)
• Example Codewords: 0000, 0001, 0010, etc.
• Parity Check:
  • Even Parity Check: Count of ones must be even for a codeword to be valid.
  • Example: 0000 (valid), 0001 (invalid).

Representation of Block Code

• Systematic codeword representation: Information bits followed by parity bits.
• Error Code: e1, e2, ..., en to identify errors.
• Valid data at the receiver: Received codeword + Error codeword (using modulo-2 addition).

Conclusion

• Block code is used in channel encoding to resolve errors caused by noise.
• Future sessions will cover types of block codes in detail.
• Encourage feedback for future improvements.