Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels

Abstract

Abstract-A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity I(W ) of any given binary-input discrete memoryless channel (B-DMC) W . The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. Channel polarization refers to the fact that it is possible to synthesize, out of N independent copies of a given B-DMC W , a second set of N binary-input channels {W

A Performance Comparison of Systematic Polar Codes and Non-systematic Polar Codes

“…The frozen bits set is denoted by the complementary set of I,i.e., I c .The reliability of ( ) i N W can be estimated by using Bhattaharyya parameter [1] for binary erasure channel (BEC). While the reliability can also be computed by density evolution or Gaussian approximation method for other channels [3] [4].…”

“…As mentioned in [1], SC decoder is considered to generate its decision In order to consider various possible systematic encoders for the code, as specified by a non-systematic encoder as in (6) [2]. In this case, after computing …”

“…Polar coding is a code construction method that can achieve the symmetric capacity ( ) I W of binary-input discrete memoryless channels [1], and polar codes in standard form are NSPCs. The codes originally introduced in [1] are a class of non-systematic linear block codes.…”

“…The codes originally introduced in [1] are a class of non-systematic linear block codes. Any linear code can be turned into a systematic code.…”

5G – Wireless Communications for 2020

“…A very promising class of codes for 5G is the so-called polar codes [80], which achieve capacity, at the cost of knowing the channel statistics a priori. These codes also have a relatively low decoder complexity, but their application in a scenario with time-varying channels and imperfect channel knowledge remains to be studied in detail.…”