Iterative encoding of low-density parity-check codes

Motivated by the potential to reuse the decoder architecture, and thus reduce circuit space, we explore the use of iterative encoding techniques which are based upon the graphical representation of the code. We design codes by identifying associated encoder convergence constraints and also eliminating some well known undesirable properties for sum-product decoding such as 4-cycles. In particular we show how the Jacobi method for iterative matrix inversion can be viewed as message passing and employed as the core of an iterative encoder. Example constructions of both regular and irregular LDPC codes that are encodable using this method are investigated.