Polarization and Polar Codes

Despite remarkable advances in the algebraic and iterative codes used in moderncommunication systems, finding codes that operate at rates close to capacity; have lowcomputational complexity; and have provable reliability guarantees was an elusive goal untilrecently. Polar Codes have all of these desirable properties. The design philosophy of polarcodes is fundamentally different from those of both algebraic codes and iterative codes. Thetechnique underlying polar codes is 'channel polarization': creating extremal channels - thosethat are either noiseless or useless - from mediocre ones.Polarization and Polar Codes is the first in-depth tutorial on this exciting newtechnique that promises to offer major improvements in digital communications systems. Thetutorial is clearly written and is accessible for all researchers and engineers who want tounderstand the fundamental concepts used in polar codes. A whole chapter is devoted todemonstrating how polar codes prove reliability using low-complexity. Generalizations of thetheory are then discussed that show how discrete memoryless processes of arbitrary alphabetsizes, not just binary ones, can be polarized by recursive transforms; how stronger codes canbe obtained by combining more than two random variables in each recursion of a polarizingconstruction; and how polar coding theorems can be used in multi-user settings.

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.