References & Further Reading

References

A. N. Kolmogorov, Foundations of the Theory of Probability, Chelsea Publishing Company, 1950
English translation of Kolmogorov's 1933 monograph Grundbegriffe der Wahrscheinlichkeitsrechnung. The original source of the axiomatic definition of probability. Remarkably short (96 pages) and still the clearest statement of the foundations.
J. A. Gubner, Probability and Random Processes for Electrical and Computer Engineers, Cambridge University Press, 2006
The primary textbook for the FSP course. Rigorous but accessible to engineers. Chapter 1 covers sample spaces, sigma-algebras, probability axioms, and combinatorics in the same order as this chapter.
P. Billingsley, Probability and Measure, Wiley, 3rd ed., 1995
The standard graduate-level reference for measure-theoretic probability. Chapter 1 gives the full measure-theoretic development of sigma-algebras and Lebesgue integration. Read this after completing FSP if you want full mathematical rigor.
W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1, Wiley, 3rd ed., 1968
The classic reference for combinatorial and discrete probability. Chapters I–II on combinatorics are the source for the sampling paradigms, birthday problem, and hypergeometric distribution in Section 1.4. Feller's exposition remains unmatched for intuition and breadth of examples.
T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley-Interscience, 2nd ed., 2006
The standard reference for information theory. The probabilistic framework in Chapter 2 (random variables, entropy) builds directly on the axioms from this chapter. The random coding argument in Chapters 7–8 uses the classical probability model from Section 1.5.
J. G. Proakis and M. Salehi, Digital Communications, McGraw-Hill, 5th ed., 2008
The standard engineering reference for digital communications. Chapter 2 reviews the probability theory used throughout the book; Section 2.1 covers the axioms informally. The union bound in Chapter 4 is the version developed in our Section 1.3.
D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005
The primary reference for wireless communication theory. The probabilistic tools from this chapter (union bound, classical model) underlie the error probability analysis throughout. Section 5.1 applies the Borel-Cantelli lemma to diversity analysis.
G. Vitali, Sul problema della misura dei gruppi di punti di una retta, Tipografia Gamberini e Parmeggiani, Bologna, 1905
The original paper constructing the Vitali set — the first non-measurable set. Demonstrates why sigma-algebras cannot simply be the power set of $\\mathbb{R}$. Historical landmark in measure theory.
A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1996. [Link]
Free online reference for cryptography. Chapter 2 covers birthday attacks and collision bounds. The birthday attack analysis in Section 1.4 follows this treatment.
G. Caire, Capacity achieving codes: A brief overview, 2021
A concise overview of random coding arguments and capacity-achieving code constructions, written by the instructor of the FSP course. Cited in the commit contribution of Section 1.5.
R. B. Ash, Basic Probability Theory, Wiley, 1970
An older but still excellent introduction to probability at the level between Feller and Billingsley. Chapter 1 covers sigma-algebras and the axioms with clear proofs and many examples.