Sequential Decoding of Polar Codes

Efficient decoding of polar codes with some 16×16 kernels

“…with BEC scaling exponent µ(K 1 ) = 3.346 [8]. Furthermore, to minimize the size of decoding windows, we derived another kernel K 2 = P σ K 1 , were P σ is a permutation matrix corresponding to permutation σ = [0, 1, 2, 7, 3, 4, 5, 6,9,10,11,12,8,13,14,15], with scaling exponent µ(K 2 ) = 3.45. Both kernels have polarization rate 0.51828.…”

Successive cancellation permutation decoding of Reed-Solomon codes

“…It was shown in [6] that the average decoding complexity can be significantly reduced at the cost of negligible performance loss if one defines path score as…”

“…Let us consider the case of sequential decoding algorithm [6], discussed in Section II-B. The idea of this approach remains valid in the case of codes over F 2 m .…”

“…Error probabilities P ′ j can be evaluated using gaussian approximation techniques [6]. In the case of transmission of the binary image of the code over a memoryless channel one obtains 1−P ′ j = (1−P j ) m , where P j is the error probability in the j-th subchannel of the polarizing transformation in the case of binary-input channel, which can be computed using density evolution [10] or Gaussian approximation [11].…”

“…The proposed method exploits representation of Reed-Solomon codes as polar codes [4] with dynamic frozen symbols [5]. This enables application of efficient sequential soft-decision decoding techniques developed in the area of polar coding [6]. Furthermore, permutation decoding techniques are utilized in order to reduce the average number of iterations performed by the sequential decoder.…”