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Batched sparse (BATS) code is a promising technology for reliable datatransmission in multi-hop wireless networks. As a BATS code consists of anouter code and an inner code that typically is a random linear network code,one main research topic for BATS codes is to design an inner code with goodperformance in transmission efficiency and complexity. In this paper, thisissue is addressed with a focus on the problem of minimizing the total numberof packets transmitted by the source and intermediate nodes. Subsequently, theproblem is formulated as a mixed integer nonlinear programming (MINLP) problemthat is NP-hard in general. By exploiting the properties of inner codes and theincomplete beta function, we construct a nonlinear programming (NLP) problemthat gives a valid upper bound on the best performance that can be achieved byany feasible solutions. Moreover, both centralized and decentralized real-timeoptimization strategies are developed. In particular, the decentralizedapproach is performed independently by each node to find a feasible solution inlinear time with the use of look-up tables. Numerical results show that the gapin performance between our proposed approaches and the upper bound is verysmall, which demonstrates that all feasible solutions developed in the paperare near-optimal with a guaranteed performance bound.

Practical Inner Codes for Batched Sparse Codes in Wireless Multihop Networks