On the Channel-Specific Construction of Polar Codes

We consider polar coding over a binary-input, discrete-output memoryless channel. We obtain bounds on the Bhattacharyya parameters of the so-called synthesized binary-input channels by using the Hamming weights of the rows of the generator matrix and the symmetric capacity of the underlying channel. Our bounds provide insight on the channel-specific construction of polar codes by showing the influence of the Hamming weight and the underlying channel. By using the new bounds one can obtain a characterization for the exponent of polar codes, where the inherent effect of the Hamming weights becomes evident.