47 february 2001 which is incorporated herein by reference in its entirety in richardson urbanke encoding the parity check matrix is divided into 6 sub matrices fig3 is a graphical representation of the division of a matrix into sub matrices according to the richardson urbanke method the shift value at the middle of b is 0 and the top value of b and d have the same values the rightmost shift value of e is 0 and the other sub matrices are zero matrices for example b t p 0 0 0 i 0 0 0 0 d p and e 0 0 0 0 i therefore et u2212 1 i i i fig4 is a graphical representation of how the codeword c is formed using computed values of p 1 and p 2 computation proceeds as follows step 4 compute p 2 t by tp 2 t au t bp t t for decoding the most common decoding algorithm is the standard belief propagation algorithm bpa or sum product algorithm spa which passes messages on the bipartite tanner graph associated with the parity check matrix see d j c mackay u201c good error correcting codes based on very sparse matrices u201d ieee trans inform theory vol 45 march 1999 which is incorporated herein by reference in its entirety for the class of quasi cyclic codes the u201c turbo decoding message passing u201d algorithm is available see m mansour and n shanbhag u201c high throughput ldpc decoders u201d ieee trans on vlsi systems vol 11.