Irregular repetition and single parity check coded BICM-ID using extended mapping -Optimal node degree allocation-

Since BICM-ID is a concatenation between channel coding and mapping, its performances strongly depend on the matching between mapping rule and code structure. In our previous papers, we proposed a yet very simple, close Shannon-limit achieving BICM-ID system. It uses very simple codes, irregular repetition and single parity check codes, combined with extended mapping. Even though we know that the key role played towards the optimal design of the proposed code is the degree allocation for variable nodes, the irregular degree allocation to the node degrees were determined only empirically, by try-and-error. This paper shows that the problem of the optimal degree allocation for the proposed BICM-ID technique can be solved by using linear programming technique. Results shows we can achieve better matching between the de-mapper and decoder curves, by which we can achieve even closer threshold to the Shannon limit and also lower error floor.