Abstract
In this paper we review existing hard-decision decoding algorithms for product codes along with different post-processing techniques used in conjunction with the iterative decoder for product codes. We improve the decoder by Reddy and Robinson and use it to create a new post-processing technique. The performance of this new post-processing technique is evaluated through simulations, and these suggest that our new post-processing technique outperforms previously known post-processing techniques which are not tailored for specific codes. The cost of using the new post-processing technique is that the algorithm becomes more complex. However, the post-processing is applied very rarely unless the channel is very noisy, and hence the increase in computational complexity is negligible for most choices of parameters. Finally, we propose a new algorithm that combines existing techniques in a way that avoids the error floor with short relatively high rate codes. The algorithm should also avoid the error floor with long high rate codes, but further work is needed to confirm this.
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Notes
Here we opportunistically assuming that the gmd decoder does not misscorrect any received word. The probability of this happening is very low when the symbol error probability is low enough.
References
Abramson, N.: Cascade decoding of cyclic product codes. IEEE Trans. Commun. Technol. 16(3), 398–402 (1968)
Blokh, E., Zyablov, V.V.: Linear Concatenated Codes. USSR, Nauka (1982)
Blomqvist, F.: pcdecode, tools for simulations with product codes (2019). https://github.com/fblomqvi/pcdecode
Condo, C., Leduc-Primeau, F., Sarkis, G., Giard, P., Gross, W.J.: Stall pattern avoidance in polynomial product codes. In: 2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP), pp. 699–702. IEEE (2016)
Elias, P.: Error-free coding. IRE Trans. Inf. Theory IT–4, 29–37 (1954)
Emmadi, S., Narayanan, K.R., Pfister, H.D.: Half-product codes for flash memory. In: Proceedings of Non-volatile Memories Workshop, vol. 312 (2015)
Ericson, T.: A simple analysis of the Blokh–Zyablov decoding algorithm. In: International Conference on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, pp. 43–57. Springer (1986)
Forney, G.D.: Concatenated codes. MIT Technical Report, 440 (1965)
Jian, Y.Y., Pfister, H.D., Narayanan, K.R., Rao, R., Mazahreh, R.: Iterative hard-decision decoding of braided bch codes for high-speed optical communication. In: 2013 IEEE Global Communications Conference (GLOBECOM), pp. 2376–2381. IEEE (2013)
Kreshchuk, A., Zyablov, V., Ryabinkin, E.: A new iterative decoder for product codes. In: Fourteenth International Workshop on Algebraic and Combinator ial Coding Theory, pp. 211–214 (2014)
Le Bidan, R., Leroux, C., Jego, C., Adde, P., Pyndiah, R.: Reed–Solomon turbo product codes for optical communications: from code optimization to decoder design. EURASIP J. Wirel. Commun. Netw. 2008, 14 (2008)
MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes, vol. 16. Elsevier, Amsterdam (1977)
Mittelholzer, T., Parnell, T., Papandreou, N., Pozidis, H.: Improving the error-floor performance of binary half-product codes. In: 2016 International Symposium on Information Theory and Its Applications (ISITA), pp. 295–299. IEEE (2016)
Pyndiah, R.M.: Near-optimum decoding of product codes: block turbo codes. IEEE Trans. Commun. 46(8), 1003–1010 (1998)
Reddy, S., Robinson, J.: Random error and burst correction by iterated codes. IEEE Trans. Inf. Theory 18(1), 182–185 (1972)
Wainberg, S.: Error-erasure decoding of product codes (corresp.). IEEE Trans. Inf. Theory 18(6), 821–823 (1972)
Wainberg, S.: Burst-error and random-error correction over q-ary input, p-ary output channels. Ph.D. dissertation, Polytech. Inst. Brooklyn (1972)
Weldon, E.: Decoding binary block codes on q-ary output channels. IEEE Trans. Inf. Theory 17(6), 713–718 (1971)
Zinoviev, V.A., Zyablov, V.V.: Decoding of non-linear generalized concatenated codes. Probl. Peredachi Inf. 14(2), 46–52 (1978)
Zinoviev, V.A., Zyablov, V.V.: Correction of error bursts and independent errors by generalized concatenated codes. Probl. Peredachi Inf. 15(2), 58–70 (1979)
Zyablov, V., Shavgulidze, S., Bossert, M.: An introduction to generalized concatenated codes. Eur. Trans. Telecommun. 10(6), 609–622 (1999)
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Blomqvist, F. On hard-decision decoding of product codes. AAECC 34, 393–410 (2023). https://doi.org/10.1007/s00200-021-00511-w
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DOI: https://doi.org/10.1007/s00200-021-00511-w