Correction of Two (or Often More) Vector Symbol Errors With the Outer Structure of a Hamming Single Error Correcting Code

The case of a concatenated code is considered where the inner code decoder reports multi-bit symbol decisions and can save the soft information used for the decision. Normally, an outer decoder using a Hamming single error correcting code cannot correct more than one error. But by using what is called soft information single error correction (SISEC) where a hypothesis that a particular symbol in some outer check set is the only error in the set can be confirmed or denied by the inner coder, a Hamming single error correcting code of any order can very easily correct, with high confidence, any pattern of two errors. In many cases > 2 errors can be corrected, up to a good fraction of even n-k errors of a (n,k) Hamming single error correcting code.