poly-adic (p-adic) extension of Projective Geometry based LDPC codes for ÔsymbolÕ error detection and correction ,on the lines of designing p-adic extensions of Hamming codes, BCH codes and Golay codes. The GraeffeÕs ÒliftingÓ method is used for obtaining p-adic extension of the codes.
For RS codes the alphabet is from the for p, a positive integer greater than 1. For 2-adic codes, the alphabet needs to be considered over the ring of 2-adic integers modulo . 2-adic codes can be decoded using probabilistic techniques (belief propagation) and therefore perform better than RS codes. RS codes are decoded using algebraic techniques.
The 2-adic extended PG based LDPC code is constructed by using simple linear shift registers and the decoding is done using the simple linear feedback symbol based shift registers. A new decoding architecture is proposed to handle the symbols apart from the bits, thus enhancing the capability of the decoder to detect different duration of burst errors and correct them.