Analysis of the Thresholds for Regular Low-Density Erasure Codes

By proving the existence of the minimum of the threshold function in (0,1) we show that the threshold of regular low-density erasure codes under erasure recovery algorithms is equal to the minimum of the threshold function in (0, 1). The existence and uniqueness of positive real root of the polynomial equation k(x) = 0 in (0,1) are verified. It follows from the two conclusions obtained above that the threshold of regular low-density erasure codes can be determined by the analytical expression.