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I am looking for a code that can correct errors with variable and limited length like huffman code. I am not an expert in coding theory. Is there any code or related literature on this?

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  • $\begingroup$ Thank you. YOu are definitely right. $\endgroup$
    – lchen
    Nov 18, 2020 at 13:31

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Variable Length Error Correction (VLEC) codes do exist, and they are used in some applications where source coding/channel coding separation may not be the best way to go and both compression and error correction is required. Here are a number of papers along this direction:

Buttigieg and Farrell, On variable-length error-correcting codes Proceedings of 1994 IEEE International Symposium on Information Theory

Savari and Kliewer, When Huffman meets Hamming: A Class of Optimal Variable-Length Error Correcting Codes, Data Compression Conference 2010, available here

Wu, Chen, Alajaji and Han, On the Design of Variable-Length Error-Correcting Codes, *IEEE Trans. Communications, 61(9),2013.

The quote below is from the last paper:

Also shown in this paper is that our VLEC system outperforms traditional separate source/channel coding systems of similar overall rate at low to medium SNRs with the benefit of considerably smaller decoding complexity.

The codes are found by search, but this is not a problem due to the existence of efficient search algorithms, and other code families are also the result of search algorithms. The decoding algorithms tend to be quite fast.

One must not forget that a lot of the mathematically beautiful algebraic codes usually do not fare so well in applications, since most channels of interest (wireless mobile) these days are not i.i.d. and gaussian but time varying.

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  • $\begingroup$ Thanks a lot. I have also done a little search at my side and found the same three papers you pointed out:) $\endgroup$
    – lchen
    Nov 18, 2020 at 13:30

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