References & Further Reading
References
- E. Ar\i kan, Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels, 2009
The original polar coding paper. Introduces channel polarization, proves capacity-achieving performance with $O(N\log N)$ encoding and decoding. Essential reading.
- C. Berrou, A. Glavieux, and P. Thitimajshima, Near Shannon Limit Error-Correcting Coding and Decoding: Turbo-Codes, 1993
The paper that launched the modern coding revolution. Demonstrates performance within 0.5 dB of the Shannon limit using iterative decoding of parallel concatenated convolutional codes.
- R. G. Gallager, Low-Density Parity-Check Codes, 1962
The original LDPC paper, far ahead of its time. Introduces sparse parity-check codes and iterative decoding. Rediscovered by MacKay and Neal in 1996.
- T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, Design of Capacity-Approaching Irregular Low-Density Parity-Check Codes, 2001
Introduces density evolution for LDPC code analysis and the optimization of irregular degree distributions to approach capacity.
- U. Erez and R. Zamir, Achieving $1/2\log(1+\text{SNR})$ on the AWGN Channel with Lattice Encoding and Decoding, 2004
Proves that nested lattice codes achieve AWGN capacity. A key result connecting algebraic coding theory with information theory.
- G. D. Forney and G. Ungerboeck, Modulation and Coding for Linear Gaussian Channels, 1998
Comprehensive treatment of the gap to capacity, decomposing it into coding gain and shaping gain. Introduces the 1.53 dB bound.
- J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, 1999
The encyclopedia of lattices. Essential reference for anyone working with lattice codes, covering $E_8$, Leech lattice, and packing/covering problems.
- G. B\"ocherer, F. Steiner, and P. Schulte, Bandwidth Efficient and Rate-Matched Low-Density Parity-Check Coded Modulation, 2015
Introduces probabilistic amplitude shaping (PAS) with the reverse concatenation architecture, enabling practical shaping with standard FEC codes.
- T. M. Cover and J. A. Thomas, Elements of Information Theory, 2006
Chapter 13 covers the Gaussian channel coding theorem. A standard reference for the theoretical foundations of this chapter.
- I. Tal and A. Vardy, List Decoding of Polar Codes, 2015
Introduces successive cancellation list (SCL) decoding for polar codes, which dramatically improves finite-length performance.
Further Reading
E. Ar\i kan, 'From Sequential Decoding to Channel Polarization and Back Again,' arXiv:1908.09594
Ar\\i kan's own retrospective on the path from sequential decoding to polar codes, providing insight into the discovery process.
S. H. Hassani, K. Alishahi, and R. L. Urbanke, 'Finite-Length Scaling for Polar Codes,' IEEE Trans. IT, 2014
Analyzes the finite-length behavior of polar codes, showing that the block error probability scales as $2^{-N^{1/2}}$ under SC decoding — important for practical code design.
T. Richardson and R. Urbanke, 'Modern Coding Theory,' Cambridge University Press, 2008
The definitive graduate textbook on iterative coding. Covers density evolution, EXIT charts, and the analysis of turbo and LDPC codes in rigorous detail.
G. B\"ocherer, 'Probabilistic Signal Shaping for Bit-Metric Decoding,' IEEE ISIT Tutorial, 2018
An accessible tutorial on probabilistic shaping, covering the PAS architecture, distribution matching, and practical implementation considerations.