Rank reduction techniques and burst error-correction decoding in real/complex fields

Previous results have shown that error-correcting codes, such as Reed-Solomon and BCH codes defined over real/complex numbers have several advantages over their counterparts in finite fields. However, in real/complex fields thecorrection of major impulsive errors have to be achieved-in the presence of minor errors in each component of the received vector, which may be due to round-off/channel noise. We device several strategies based on two least squares techniques and singular value decomposition based techniques to achieve good error correction. A particularly useful technique for correcting burst errors based on rearranging the parity frequencies is also suggested