Multivariate interpolation decoding of heterogeneous Interleaved Reed-Solomon codes

We derive and analyze an algorithm for collaborative decoding of heterogeneous Interleaved Reed-Solomon (IRS) codes. In order to generate IRS codes, several codewords from different RS codes with the same length over the same Galois field are interleaved. The basis of the decoding algorithm is similar to the Guruswami-Sudan (GS) decoding method. However, here multivariate interpolation is used in order to decode all the codewords of the interleaved scheme simultaneously. In the presence of burst errors, it is shown that the error correction capability of this algorithm is larger than that of independent decoding of each codeword using the standard GS method. In the latter case, the error correction capability is equal to the decoding radius of the GS algorithm for the RS code with the largest dimension.