This course introduces the foundations of classical communication systems and information theory, providing a basis for the study of quantum communication. Starting from the components of a digital communication system, we study how information is represented by signals, transmitted over noisy channels, and recovered at the receiver. We develop the tools needed to analyze modulation, filtering, detection, and error probability, and then introduce channel coding and the tradeoff between transmission rate and reliability. Entropy, mutual information, and channel capacity provide a framework for understanding the fundamental limits of reliable communication. Finally, we study practical error-correcting codes and introduce connections with quantum detection and quantum information theory.

Students will acquire an understanding of:

  • The fundamental elements and probabilistic modeling of classical communication systems.

  • Modulation, filtering, and detection techniques, and their performance in the presence of noise.

  • Information measures and the fundamental limits of reliable communication.

  • Channel coding, linear block codes, and error-correction techniques.

Program

Unit 1. Communication Systems. Analog and digital communication, modulation and demodulation, and pulse amplitude modulation.

Unit 2. Modulation and Filtering. Fourier transforms, linear time-invariant systems, matched filtering, frequency translation, and quadrature amplitude modulation.

Unit 3. Noise. Random variables, Gaussian noise, probabilistic bounds, and memoryless channel models.

Unit 4. Detection. Hypothesis testing, maximum-likelihood and maximum a-posteriori detection, nearest-neighbor decoding, and error probability of PAM/QAM. Connections with quantum detection.

Unit 5. Channel Coding. Repetition codes, coding rate, the tradeoff between rate and reliability, and the channel coding theorem.

Unit 6. Information Theory. Entropy, conditional entropy, mutual information, and channel capacity. Introduction to quantum information theory.

Unit 7. Error Correction. Linear block codes, generator and parity-check matrices, syndrome decoding, Hamming codes, soft-decision decoding, and error-detection and error-correction capabilities.

Course material

  • Class notes with detailed derivations, available through Aula Global.

  • Problem sets to practice and deepen understanding of the course material.