Chapter 17Polar Codes
17.1 Introduction and Preview
Polar codes, invented by Erdal Arıkan, are the first family of codes proven to achieve Shannon channel capacity. The codes have low encoding and decoding complexity: for a code of length 
, both the encoding and the decoding complexity is 
. Unlike many modern codes such as turbo codes or LDPC codes, decoding is noniterative. There are explicit code design algorithms and there is great flexibility in selection of the rate for virtually any rate below the channel capacity.
As an introduction, Figure 17.1 highlights some aspects of the probability of error performance of polar codes. In Figure 17.1(a), frame error rates and bit error rates for a rate 
code of a “moderate” length of 
are shown. The red line shows the performance of the basic “successive cancellation” (SC) decoder, the 
decoder originally proposed. This is described in Section 17.4.7. Also shown is the result of list decoding for list sizes of , and 32. List decoding provides ...
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