Lec 28: Probability of Error for QAM

Lec 28: Probability of Error for QAM

by Prof. Ribhu

Formal & Physical Sciences Engineering & Technology TJKCommunications engineering
🎙 Prof. Ribhu 👥 226K 📅 July 31, 2026 ⏱ 16 min 👁 35 📄 lecture 🧭 2026-08-02
Available in: English (current) Français

Keywords

QAMprobability of errordecision regionsrectangular QAMunion bound

Summary

This lecture, part of the NPTEL course ‘Analog and Digital Communications II’, focuses on calculating the probability of error for Quadrature Amplitude Modulation (QAM). The instructor begins by reviewing the probability of error for PM and PSK, noting the difficulty of solving the integral for PSK. He then introduces QAM, representing symbols as sm = am e^{jθ}. He discusses rectangular QAM as a special case, where the in-phase and quadrature components are independent PM constellations. For rectangular QAM, the probability of error can be computed by treating the I and Q components separately, since they are independent. The overall error probability is then 1 - (1 - PeI)(1 - PeQ). However, for general QAM constellations, such as those combining PSK with different energies, the decision regions become complex and the components are not independent, making the error probability calculation difficult. The lecture concludes by mentioning that the union bound will be derived in the next lecture as a potential solution to this problem.

163 words

Critical Evaluation

The lecture provides a clear and rigorous derivation of the probability of error for rectangular QAM, leveraging the independence of in-phase and quadrature components. The instructor effectively explains the limitations of this approach for general QAM constellations, setting the stage for the union bound. The mathematical explanations are precise, and the use of diagrams (though not visible in the transcript) likely aids understanding. The content is well-structured, starting with a review of previous concepts and building up to the current topic. The source is a formal educational lecture from a reputable institution, ensuring high reliability. The main limitation is the lack of concrete examples or numerical illustrations, which could enhance comprehension. Additionally, the lecture is part of a series, so it assumes prior knowledge from previous lectures, which may not be suitable for standalone viewing. Overall, the lecture is technically sound and valuable for students of digital communications.

148 words

Title / Content Match

The title accurately reflects the content, which focuses on deriving the probability of error for QAM modulation.

Quality & Reliability

8/10

Lecture by a professor from IIT Guwahati, part of a formal NPTEL course. The content is mathematically rigorous, with derivations and explanations of concepts. The source is institutional and reliable.

Key Moments

Markers derived by PSI from the transcript: the creator did not define chapters.

Cited Sources

Concurring Sources

Contribution & Novelties

This lecture provides a clear pedagogical explanation of the probability of error for QAM, particularly highlighting the simplification for rectangular QAM due to independence of I and Q components. It sets the stage for the union bound as a general solution.

Pour aller plus loin :

94 words

Radar Profile

The radar profile shows a balanced performance across all dimensions, with slightly higher scores in technical level and reliability, reflecting the formal academic nature of the lecture. The lower score in quantity of information is due to the short duration and focused scope.

Reliability 8/10