References & Further Reading

References

  1. Y. Polyanskiy, H. V. Poor, and S. Verdu, Channel Coding Rate in the Finite Blocklength Regime, 2010

    The foundational paper on finite-blocklength information theory. Introduces the RCU bound, meta-converse, and normal approximation. Essential reading.

  2. Y. Polyanskiy, Channel Coding: Non-Asymptotic Fundamental Limits, PhD thesis, Princeton University, 2010

    The complete treatment, including extensions to feedback, variable-length codes, and multi-user channels. More detailed than the journal paper.

  3. V. Strassen, Asymptotische Abschatzungen in Shannons Informationstheorie, 1962

    The pioneering work establishing the second-order rate for the BSC. Largely forgotten for 45 years until rediscovered in the context of URLLC.

  4. M. Hayashi, Information Spectrum Approach to Second-Order Coding Rate in Channel Coding, 2009

    Independent derivation of the second-order rate using the information spectrum method. Covers general (non-stationary, non-ergodic) channels.

  5. E. MolavianJazi and J. N. Laneman, A Second-Order Achievable Rate Region for Gaussian Multi-Access Channels via a Central Limit Theorem for Functions, 2015

    Extends the normal approximation to the Gaussian MAC. Derives the dispersion matrix and second-order rate region.

  6. V. Y. F. Tan, Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities, Foundations and Trends in Communications and Information Theory, vol. 11, no. 1-2, 2014

    Comprehensive monograph on second-order asymptotics for channels and sources. Covers BC, MAC, wiretap channel, and source coding.

  7. G. Durisi, T. Koch, and P. Popovski, Toward Massive, Ultrareliable, and Low-Latency Wireless Communication with Short Packets, 2016

    Bridges finite-blocklength theory and 5G URLLC system design. Excellent overview of how the PPV bounds inform practical engineering decisions.

  8. Y. Polyanskiy, A Perspective on Massive Random Access, 2017

    Introduces the many-access regime where the number of users grows with blocklength. Derives fundamental limits on energy-per-bit in grant-free access.

  9. J. Scarlett, A. Martinez, and A. Guillen i Fabregas, Mismatched Decoding: Error Exponents, Second-Order Rates and Saddlepoint Approximations, 2017

    Extends finite-blocklength analysis to mismatched decoding, relevant for practical systems where the decoder assumes a different channel model.

Further Reading

For readers who want to go deeper into specific topics from this chapter.

  • Finite-blocklength source coding

    V. Kostina and S. Verdu, 'Fixed-Length Lossy Compression in the Finite Blocklength Regime,' IEEE Trans. Inf. Theory, vol. 58, no. 6, pp. 3309-3338, Jun. 2012

    The source-coding analog of the PPV channel coding result. Shows that rate-distortion theory has a similar $\sqrt{V/n}$ correction, completing the finite-blocklength picture.

  • Saddlepoint approximations for channels

    J. Font-Segura, G. Vazquez, and A. Martinez, 'Saddlepoint Approximation of the Coding Rate for a Given Error Probability,' IEEE ISIT 2018

    More accurate than the normal approximation at short blocklengths ($n < 100$), where the CLT approximation of the information density is loose.

  • Finite-blocklength MIMO

    W. Yang, G. Durisi, T. Koch, and Y. Polyanskiy, 'Quasi-Static Multiple-Antenna Fading Channels at Finite Blocklength,' IEEE Trans. Inf. Theory, vol. 60, no. 7, pp. 4232-4265, Jul. 2014

    Extends the PPV framework to MIMO fading channels. Essential for URLLC design with multi-antenna systems.

  • Age of information and short packets

    R. D. Yates, Y. Sun, D. R. Brown, S. K. Kaul, E. Modiano, and S. Ulukus, 'Age of Information: An Introduction and Survey,' IEEE JSAC, vol. 39, no. 5, pp. 1183-1210, May 2021

    Connects finite-blocklength coding to the age-of-information metric, which captures timeliness rather than just throughput. Relevant for real-time IoT applications.

  • Coded random access

    A. Fengler, P. Jung, and G. Caire, 'SPARCs and AMP for Unsourced Random Access,' IEEE Trans. Inf. Theory, vol. 67, no. 12, pp. 7840-7862, Dec. 2021

    State-of-the-art coding scheme for the many-access channel, achieving near-optimal energy efficiency with short packets. Connects to the CommIT group's work on massive random access.

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