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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.

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    $\begingroup$ 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/… $\endgroup$ – leonbloy Mar 8 '18 at 20:11
  • $\begingroup$ @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. $\endgroup$ – Chris LIU Mar 9 '18 at 6:05

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