Study on the Performance of SPC Product Codes
Palavras-chave:
SPC product codes, error detection, erasure patterns, bipartite graphs, binary matricesResumo
The single parity-check (SPC) code is a very popular MDS error detection code, since it is very easy to implement. One bit is appended to an information sequence of length n−1, such that the resultant codeword has an even number of ones. Two SPC codes can be used jointly to obtain an SPC product code, which has a minimum distance of 4. Therefore, it can recover all erasure patterns with one, two or three erasures over the erasure channel. However, in some special cases, patterns of up to 2n − 1 erasures can be corrected. Furthermore, a codeword of length n² can be represented by an erasure pattern of size n × n, where the only information considered is the position of the erasures.
Downloads
Referências
S. D. Cardell and J. J. Climent. “An approach to the performance of SPC product codes on the erasure channel”. In: Advances in Mathematics of Communications 10.1 (2016), pp. 11–28. doi:10.3934/amc.2016.10.11.
S. D. Cardell, J. J. Climent, and A. López Martín. “SPC product codes, graphs with cycles and Kostka numbers”. In: RACSAM 113 (2019), pp. 3751–3765. doi:10.1007/s13398-019-00698-1.
P. Elias. “Coding for noisy channels”. In: IRE International Convention Record, pt. 4. 1955, pp. 37–46.
L. Hogben. Handbook of Linear Algebra. Chapman and Hall/CRC, 2007. isbn:978-1-58488-510-8.
M. A. Kousa. “A novel approach for evaluating the performance of SPC product codes under erasure decoding”. In: IEEE Transactions on Communications 50.1 (2002), pp. 7–11. doi:10.1109/26.975732.
