  A method for efficiently successive cancellation (SC) decoding of polar codes
with high-dimensional linear binary kernels (HDLBK) is presented and analyzed.
We devise a $l$-expressions method which can obtain simplified recursive
formulas of SC decoder in likelihood ratio form for arbitrary linear binary
kernels to reduce the complexity of corresponding SC decoder. By considering
the bit-channel transition probabilities $W_{G}^{(\cdot)}(\cdot|0)$ and
$W_{G}^{(\cdot)}(\cdot|1)$ separately, a $W$-expressions method is proposed to
further reduce the complexity of HDLBK based SC decoder. For a $m\times m$
binary kernel, the complexity of straightforward SC decoder is $O(2^{m}N\log
N)$. With $W$-expressions, we reduce the complexity of straightforward SC
decoder to $O(m^{2}N\log N)$ when $m\leq 16$. Simulation results show that
$16\times16$ kernel polar codes offer significant advantages in terms of error
performances compared with $2\times2$ kernel polar codes under SC and list SC
decoders.
