Analysis of regular low-density erasure codes

A detailed study of low-density erasure codes based on regular sequences of degree distribution is made. By analyzing regular sequences of degree distribution in detail a result is presented on the maximum tolerable loss fraction for regular low-density erasure codes. By using this result the relationship of two thresholds δ^* (3, 6) and δ^* (d, nd) is given for (3,6) and (d, nd)-regular degree distributions (d≥3, n≥2). In the meantime, it is shown that low-density erasure codes based on (d, 2d)-regular sequences of degree distribution are not close to optimum from the theoretical point of view of theory. Moreover, the simulation and intuition are given as to why regular codes are not close to optimum. These analyses will be helpful in designing the sequences of degree distribution for low-density erasure codes.