Analysis for rank distribution of BATS codes under time-variant channels

Abstract

As a two-step coding technique applied in multi-hop networks with a low complexity, the transmission performance of batched sparse (BATS) code was directly related to the rank distribution of the transfer matrix.Based on the assumption that the packet loss rate of each link on the erasure channel was constant, the rank distribution of the batch sparse codes on the erasure correction channel had been widely studied.However, in some scenarios such as the industrial Internet, a large number of mobile nodes were deployed in the whole network, which may cause the channels among nodes to become time-varying, that was, the packet loss rate on the link may vary with time.Therefore, under the assumption that the link packet loss rate between nodes in the network changes randomly, the rank distribution of batched sparse code transmission matrix was studied when random linear network coding (RLNC) and system recoding were used as inner coding schemes, and the closed solution of normalized rank expectation was deduced when the link packet loss rate obeyed the finite interval normal distribution.The correctness of the closed solutions was verified by Monte Carlo simulation.

Keywords

• BATS code
• random linear network coding
• system recoding
• rank distribution
• time-variant channel