References & Further Reading

References

1. C. E. Shannon, A Mathematical Theory of Communication, 1948

   The founding paper of information theory. Derives the AWGN capacity formula and proves both achievability and converse. Essential reading for any information theorist.

2. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2006

   The standard graduate textbook. Chapter 9 covers the Gaussian channel, parallel channels, and water-filling with full proofs and worked examples.

3. R. G. Gallager, Information Theory and Reliable Communication, 1968

   Gallager's classic text provides an alternative development of Gaussian channel capacity with emphasis on error exponents and the sphere-packing bound.

4. G. Caire, G. Taricco, and E. Biglieri, Bit-Interleaved Coded Modulation, 1998

   Introduces the mutual information analysis of BICM, connecting practical coded modulation to the parallel channel framework.

5. A. Goldsmith, Wireless Communications, 2005

   Chapters 4 and 9 provide an accessible treatment of the AWGN capacity and its application to wireless link budget design.

6. D. Tse and P. Viswanath, Fundamentals of Wireless Communications, 2005

   Chapter 5 covers the AWGN channel capacity with a wireless communication perspective, including the bandwidth-power tradeoff and OFDM.

7. J. G. Smith, The Information Capacity of Amplitude- and Variance-Constrained Scalar Gaussian Channels, 1971

   Shows that under a peak power constraint, the capacity-achieving input distribution is discrete with a finite number of mass points.

8. A. El Gamal and Y.-H. Kim, Network Information Theory, 2011

   Chapter 3 provides a rigorous treatment of the Gaussian channel using the entropy power inequality. A modern reference for advanced topics.

9. S. Verdu, Spectral Efficiency in the Wideband Regime, 2002

   Characterizes capacity per unit cost in the wideband limit. Shows that orthogonal signaling is first-order optimal at low SNR.

10. A. Lapidoth, A Foundation in Digital Communication, 2017

    An alternative development of Gaussian channel capacity that avoids differential entropy, using sphere-packing arguments directly.

Further Reading

• R. G. Gallager, 'Information Theory and Reliable Communication,' Ch. 7-8

  Provides a rigorous treatment of the sphere-packing bound and random coding error exponents for the Gaussian channel, going beyond the capacity result to characterize the error probability at finite block length.

• S. Verd\'u, 'Spectral Efficiency in the Wideband Regime,' IEEE Trans. IT, 2002

  Characterizes the capacity per unit cost (energy efficiency) in the wideband limit and shows that orthogonal signaling is first-order optimal in the low-SNR regime.

• A. Lapidoth, 'A Foundation in Digital Communication,' Ch. 16-18

  Provides an alternative development of the Gaussian channel that avoids differential entropy and uses the mutual information directly via sphere-packing arguments.

• D. Tse and P. Viswanath, 'Fundamentals of Wireless Communications,' Ch. 5

  Covers the OFDM connection to parallel Gaussian channels and water-filling with practical wireless communication examples.