Practical Inner Codes for Batched Sparse Codes

Batched sparse (BATS) code is a promising technology for reliable end-to-end transmission in multi-hop wireless networks. One main research topic for BATS code is how to design an optimal inner code that is typically random linear network code. In this paper, this issue is focus on the number of transmissions from an end-to-end perspective. The problem is formulated as a mixed integer nonlinear programming (MINLP) problem with the objective of minimizing the total number of transmissions from source to destination. Subsequently, the inherent properties of inner codes are exploited to relax the integer restrictions by the means of the regularized incomplete beta function. As a result, a new nonlinear programming (NLP) problem is constructed. Solving the NLP problem provides a valid lower bound on the optimal solution, and, hence, is used as the performance measure for our heuristic. Furthermore, a centralized approximation approach is developed to solve our MINLP problem efficiently. The numerical results demonstrate that all solutions developed in the paper are near-optimal with a guaranteed performance bound.