A New Method for the Decoding Delay Distributions of Random Linear Coding Schemes

In this letter, we introduce a new technique for deriving the exact decoding delay distribution expressions of random linear coding schemes over a lossy channel. Our approach is mainly based on two transformations: on the one hand, from an overall perspective, the correspondence between the calculation of the exact decoding delay distribution over a perfect channel and the counting problem for some special matrices can be established. On the other hand, the relationship between some cardinalities of the special matrices and the typical basis of polynomials can be obtained. Last, the decoding delay distribution issues can be solved by employing the polynomial basis representation method.