# What is the error-correcting capacity (randomly errors, or burst errors) of polar code?

Polar codes, invented by Arikan, with low encoding and decoding complexity. But the minimum distance of polar codes is not great. The normalized minimum distance goes to $0$ with the block size. Yet, the existing decoding algorithms for polar codes can asymptotically achieve channel capacity.

Generally, a code with minimum distance $d$ can correct $\frac{d-1}{2}$ errors (random errors). And Polar code is also error-correcting code, I was wondering how many errors can it correct( e.g. A $[2048, 614]$ with $BEC(0.19)$ polar code.)? Much appreciated.

• To ask for "how many errors can a code correct", if by that we assume (as usual) the maximal amount of errors that the code can guarantee to correct - then the answer is simply $(d−1)/2$, so your question is equivalent to ask about the minimum distance of that code. Someone might answer that.Notice however that this is not the ultimate measure of how good a code is. What matters is the global probability of decoding error. Modern codes (as Polar codes) intend to dispell that "obsession with distance". math.stackexchange.com/questions/1843604/… – leonbloy Mar 8 '18 at 20:11
• @leonbloy, thanks for the reply.Yes, the polar code does not depend on the distance. BTW, how can I compute the probability of decoding error (e.g. Successive cancellation decoder)? Thx. – Chris LIU Mar 9 '18 at 6:05