Vector symbol decoding with list inner symbol decisions

Vector symbol decoding is an outer code decoding technique for a concatenated code which works with a (n-k)*r syndrome matrix S of n-k linear combinations of r-bit inner code symbol vectors. A Gauss-Jordan reduction provides an error location vector. The zeros in the error location vector are the apparent error positions, and the number of zeros should match the rank of S. Then the error values can be solved. Decoding success is related to the linear independence of error vectors. Data scrambling techniques for inner code symbols can make linear independence likely for moderately large r. Any parity check code structure can be used for the combination rules. The new result is that, if the outer code decoder has available a (possibly ordered) list of two or more alternative decisions for some or all inner symbols, a slightly modified vector symbol decoder automatically reveals most correct alternatives, allowing more powerful and often simpler correction. Moreover, the ability to recognize these alternatives does not require error vector linear independence. The main idea is to store differences between alternative choices and the first choice as additional rows below the syndrome matrix S