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Despite remarkable advances in the algebraic and iterative codes used in modern
communication systems, finding codes that operate at rates close to capacity; have low
computational complexity; and have provable reliability guarantees was an elusive goal until
recently. Polar Codes have all of these desirable properties. The design philosophy of polar
codes is fundamentally different from those of both algebraic codes and iterative codes. The
technique underlying polar codes is 'channel polarization': creating extremal channels - those
that are either noiseless or useless - from mediocre ones.
Polarization and Polar Codes is the first in-depth tutorial on this exciting new
technique that promises to offer major improvements in digital communications systems. The
tutorial is clearly written and is accessible for all researchers and engineers who want to
understand the fundamental concepts used in polar codes. A whole chapter is devoted to
demonstrating how polar codes prove reliability using low-complexity. Generalizations of the
theory are then discussed that show how discrete memoryless processes of arbitrary alphabet
sizes, not just binary ones, can be polarized by recursive transforms; how stronger codes can
be obtained by combining more than two random variables in each recursion of a polarizing
construction; and how polar coding theorems can be used in multi-user settings.
List of contents
1. Introduction 2. Polarization and Polar Coding 3. Complexity 4. Processes with Arbitrary Alphabets 5. Generalized Constructions 6. Joint Polarization of Multiple Processes 7. Conclusion and Related Work. References.
