Structured LDPC over urn model channels with memory

In this paper we investigate the performance of structured LDPC codes over a class of channels with memory. The channels under consideration are based on Polya´s urn model (F.Alajaji et al, IEEE Trans. Inform. Theory, vol.40, no.6, p.2035-2041, 1994) and can be viewed as a practical representative of channels with burst errors. The BER curves for iterative decoding with channel estimation show that random-like codes and a new class of regular and irregular codes, based on parity-check matrices of the form of block-circulants, have comparable performance for codelengths of the order of several thousands. Furthermore, the complete convergence region within the parameter space of the urn channel model is determined by using a new technique for generating side-information, termed state XORing. This technique also allows for complete characterization of the convergence region of another important bursty channel model, namely the Gilbert-Eliot scheme. Some possible applications of the results described in this paper are for designing reliable coding schemes for communication over fading or storage channels.