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Improved upper bounds on the blocklength required to communicate over binary-input channels using polar codes, below some given error probability, are derived. For that purpose, an improved bound on the number of non-polarizing channels is obtained. The main result is that the blocklength required to communicate reliably scales at most as O((I(W ) -(More)
The problem of low-complexity linear programming (LP) decoding of nonbinary low-density parity-check (LDPC) codes is considered, and an iterative LP decoding algorithm is presented. Results that were previously derived for binary LDPC codes are extended to the nonbinary case. Both simple and generalized nonbinary LDPC codes are considered. It is shown how(More)
The polarization process of polar codes over a ternary alphabet is studied. Recently it has been shown that the scaling of the blocklength of polar codes with prime alphabet size scales polynomially with respect to the inverse of the gap between code rate and channel capacity. However, except for the binary case, the degree of the polynomial in the bound is(More)
Linear codes constructed using a polarization transformation followed by short blocklength sub-codes are proposed. Decoding is realized by the successive cancellation algorithm combined with standard optimal or non-optimal decoding of the sub-codes. List successive cancellation decoding can also be used. We demonstrate gains compared to standard successive(More)
A concatenated coding scheme, recently proposed by Mahdavifar et al., is considered. The scheme uses polar codes as inner codes and maximum distance separable codes, such as Reed-Solomon codes, as outer codes. It was shown by Mahdavifar et al. that the concatenated coding scheme has a significantly better asymptotic error decay rate compared to Arikan's(More)
Polar code-based source coding is considered for some given code rate and some desired distortion level. The distortion level of a typical quantized source vector is required to be below the desired distortion level. A sufficient polynomial scaling law of the blocklength with respect to the gap between the desired distortion and the distortion-rate function(More)
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