Understanding Convolutional Codes and Trellis Coded Modulation — Lesson 4

This lesson covers the concept of convolutional codes and trellis coded modulation in wireless communications. It begins with an introduction to convolutional codes, which are error control codes with memory. The lesson then delves into trellis codes and the standard decoding procedure for these codes, known as Viterbi decoding. The lesson also touches on trellis coded modulation, which combines error control coding with modulation. The lesson further explains the concept of free Euclidian distance, asymptotic coding gain, and the process of mapping by set partitioning. It concludes with a summary of the key points discussed.

Video Highlights

00:59 - Introduction to the lecture on wireless communications and the topic of convolutional codes
03:10 - Explanation of the concept of memory in coding and its significance
07:45 - Discussion on the concept of trellis diagram and its importance in understanding the encoding process
09:12 - Explanation of the encoding process using a trellis diagram
23:54 - Discussion on the concept of generator polynomial matrix in convolutional codes
28:09 - Explanation of the concept of free distance in convolutional codes
36:09 - Discussion on the concept of trellis coded modulation and its advantages
42:07 - Explanation of the concept of free Euclidean distance in trellis coded modulation
52:02 - Summary of the lecture and the topics covered

Key Takeaways

- Convolutional codes are a class of error control codes with memory.
- Trellis codes and Viterbi decoding are essential components of convolutional codes.
- Trellis coded modulation combines error control coding with modulation for enhanced performance.
- Free Euclidian distance and asymptotic coding gain are important concepts in understanding the performance of trellis coded modulation.
- The process of mapping by set partitioning is used in trellis coded modulation.