Spatial coupling of root-LDPC: Parity bits doping

Random low-density parity-check (LDPC) ensembles do not achieve full diversity on block-fading channels. To cope with quasi-static fading, a special LDPC structure, known as root-LDPC, has been introduced. A root-LDPC ensemble guarantees that any information bit receives messages from all channel states. Results in the literature show that the gap between the root-LDPC boundary and the capacity boundary in the fading plane is not small enough. In this paper, we propose to saturate the whole root-LDPC boundary via spatial coupling. For simplicity, we adopt an equivalent erasure channel model rather than a block fading model. It is shown that spatial coupling of parity bits only is sufficient to saturate the root-LDPC threshold boundary in the erasure plane.