The Polynomial of correctable 2 Concatenated codes patterns of concatenated codes Let B(n
Nicolas Seiidrier · 1992
The polynomial of correctable patterns is defined In [l] as the weight enumerator of the set of error patterns correctable by a given decoding algorithm. The polynomials of uncorrectable and miscorrected patterns can be defined as well ([5] aid (61) These polynomials allow a compact representation of a decodiilg alient to compute the coriection probabillty and ability thiougli a memoryless symetric channel. Our purpose heie is to compute the polynomials of correctable patThese results are geneialised in [5] and [SI for erasure channels. terns of concatenated codes for dlffeient decoding algorithms. I) We give the weight distribution of the erior patterns correctable by the standard decoding algorithm. * We give bounds for the weight distribution of the error patterns correct able by Block- Zyablov algorithm. This new method for evaluating concatenated codes will thus provide to evaluate the standard algorithm. It will also give a with precision the performances of the Block-Zyablov decoding algorithm which needed, up to llow, a (much more expensive) simulation. ill compute the decoding performances of the rdstrom-Robinson ([4, p. 731) inlier code, and a Reed-Solomon (255,223,33) outer code over F2~6.