Finite-Geometry Low-Density Parity-Check Codes for Channels with Stuck-at Defects

We investigate the use of finite-geometry low-density parity-check (FG-LDPC) codes for channels with stuckat defects. Such a channel is corrupted by a stuck-at defect pattern in addition to the usual channel-induced noise. When the defect pattern is known to the encoder but not to the decoder, the capacity of the channel is the same as if the defect pattern were also revealed to the decoder. Capacity-achieving codes for such channels require a good quantization code embedded inside a good errorcorrecting code. The main idea of this paper is that such an embedding may be realized by taking advantage of the cyclic or quasi-cyclic structure of FG-LDPC codes, which allows a quantization codes with low trellis complexity to be constructed. Combining this with the good errorcorrecting capability of low-density parity-check codes, we demonstrate that FG-LDPC codes offers good performance on channels with stuck-at defects.