675 research outputs found
Properties and Construction of Polar Codes
Recently, Ar{\i}kan introduced the method of channel polarization on which
one can construct efficient capacity-achieving codes, called polar codes, for
any binary discrete memoryless channel. In the thesis, we show that decoding
algorithm of polar codes, called successive cancellation decoding, can be
regarded as belief propagation decoding, which has been used for decoding of
low-density parity-check codes, on a tree graph. On the basis of the
observation, we show an efficient construction method of polar codes using
density evolution, which has been used for evaluation of the error probability
of belief propagation decoding on a tree graph. We further show that channel
polarization phenomenon and polar codes can be generalized to non-binary
discrete memoryless channels. Asymptotic performances of non-binary polar
codes, which use non-binary matrices called the Reed-Solomon matrices, are
better than asymptotic performances of the best explicitly known binary polar
code. We also find that the Reed-Solomon matrices are considered to be natural
generalization of the original binary channel polarization introduced by
Ar{\i}kan.Comment: Master thesis. The supervisor is Toshiyuki Tanaka. 24 pages, 3
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