A lower bound on achievable rates by polar codes with mismatch polar decoding

In this paper we show that mismatched polar codes over symmetric B-DMCs symmetrized under the same permutation can achieve rates of at least I(W, V) bits whenever I(W, V) > 0, where W denotes the communication channel, V the mismatched channel used in the code design including both the encoder and decoder, and I(W, V) × Σ
_y
Σ
_{x ϵ {0,1}}
1/2 W(y|x) log
₂
(V(y|x))/(1/2V(y|0) + 1/2V(y|1)).