Digital Communication Playlist: Block Code Basics

Introduction

• Session presented by Professor Hitesh Dhodakia
• Focus on the basics of block code in digital communication
• Series of sessions planned for comprehensive understanding of block code

Session Outlines

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

Basics of Channel and Code Word

• Every channel has an upper limit on information transmission rate (channel capacity).
• Channels include: optical fiber, wireless, coaxial cable.
• Channel capacity: The maximum rate at which information can be transmitted reliably.
• Noise causes errors in received signals; thus, reliable data transmission requires error correction.

Block Code

• Definition: A block code is a set of words with a fixed number of bits, defined by mathematical properties.
• Words in block code are termed codewords.
• Codewords sent and received help correct errors up to a certain extent.

Structure of Communication System

• Transmitter:
  • Contains:
    • Source Encoder
    • Channel Encoder (where block code is added)
    • Modulator
• Receiver:
  • Contains:
    • Demodulator
    • Channel Decoder
    • Source Decoder
• Signal Transmission: Noise may be added during transmission, leading to errors.

Channel Encoding and Block Code

• Source Encoding: Reduces redundancy to improve bandwidth utilization (does not correct errors).
• Channel Encoding: Corrects errors by adding block code.
• Block code is used specifically in the channel encoder.

Understanding Block Code Parameters

• Information bits (K) and parity bits (R) formulate block code:
  • Total bits (N) = K + R
  • Block code represented as (n, k) where:
    • n = total bits
    • k = information bits
    • R = n - k (redundancy)
• Types of codewords:
  • Systematic Codewords: Information bits kept together with parity bits.
  • Non-Systematic Codewords: Information bits and parity bits arranged randomly.

Important Block Code Parameters

• Total codewords for n bits: 2^n
• Total codewords for k information bits: 2^k
• Total redundant codewords: 2^(n-k)
• Code Rate (r): k/n

Example: 4,3 Block Code

• 4,3 Block Code: 4 total bits, 3 information bits, 1 parity bit.
• Codewords generated for even parity check to ensure accuracy.
• If a codeword has an even number of ones, it is a correct codeword; otherwise, it is false.
• Odd parity check has similar principles but focuses on odd counts of ones.

Code Representation

• Information bits: I1 to IK
• Parity bits: P1 to PR
• Systematic codeword format: Information bits followed by parity bits.
• Error detection via bitwise operations (modulo 2 addition) to identify and potentially correct errors.

Conclusion

• Block codes are crucial for error correction in channel encoding.
• Future sessions will cover different types of block codes in detail.
• Suggestions and feedback are encouraged for further video improvements.