The SC–ML dominance conjecture for polar codes under list decoding

Consider two polar codes $A$ and $B$ with the same code length $n$ and message length $k$. Let ${\rm FER_{SC}}(\cdot)$ and ${\rm FER_{ML}}(\cdot)$ denote their frame-error rates under successive-cancellation and maximum-likelihood decoding, respectively. SC–ML dominance conjecture. If either

$${\rm FER_{SC}}(A) \leq {\rm FER_{SC}}(B),\qquad {\rm FER_{ML}}(A) < {\rm FER_{ML}}(B),$$

or

$${\rm FER_{SC}}(A) < {\rm FER_{SC}}(B),\qquad {\rm FER_{ML}}(A) \leq {\rm FER_{ML}}(B),$$

then code $A$ outperforms code $B$ for every list size $L\in(1,2^k)$ at high signal-to-noise ratio. The paper illustrates this with polar codes having similar AUBs and compares their performance for small and large list sizes.