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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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I am not an expert but I think you may be asking the wrong question. Polar codes don't have a meaningful "error correction capability" obtainable as in algebraic codes by (d-1)/2. Alternatively, this is not the meaningful parameter of significance.

For finite lengths their performance is usually analyzed in BEC (Binary Erasure Channel) and AWGN channels (Additive White Gaussian Noise). The well-cited paper On Finite-Length Performance of Polar Codes: Stopping Sets, Error Floor, and Concatenated Design by A. Eslami and H. Pishro-Niki on arxiv here as well as some more recent papers confirm this.

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  • $\begingroup$ Thank you very much for the kind reply, Let me check the reference. Thanks. $\endgroup$ – Chris LIU Mar 15 '18 at 5:06

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