This book explains the philosophy of the polar encoding and decoding
technique. Polar codes are one of the most recently discovered
capacity-achieving channel codes. What sets them apart from other
channel codes is the fact that polar codes are designed mathematically
and their performance is mathematically proven.
The book develops related fundamental concepts from information theory,
such as entropy, mutual information, and channel capacity. It then
explains the successive cancellation decoding logic and provides the
necessary formulas, moving on to demonstrate the successive cancellation
decoding operation with a tree structure. It also demonstrates the
calculation of split channel capacities when polar codes are employed
for binary erasure channels, and explains the mathematical formulation
of successive cancellation decoding for polar codes. In closing, the
book presents and proves the channel polarization theorem, before
mathematically analyzing the performance of polar codes.