Storage and Communication Tradeoff for Wireless Coded Blockchains

Recently, coded blockchain systems have been proposed to encode blockchain into coded fragments and distributively store them. These fragments can be collected and decoded to obtain the original blockchain only when needed. This reduces the storage requirement of blockchains and makes it possible to incorporate blockchain in wireless Internet-of-things systems. However, transmitting such coded fragments consumes nonnegligible resource in wireless networks. Hence, this paper studies the storage and transmission trade-off for coded blockchains, and formulates the coded fragments assignment using an integer linear program (ILP). In particular, a Q-hop localization property is proposed to ensure that any device is able to collect sufficient coded fragments for decoding within Q-hop neighbors. This paper then proposes an efficient heuristic algorithm that is built upon the solution to the relaxed ILP. Apart from these, this paper studies regrowing blockchains, where nodes dynamically join and leave the networks, and proposes an algorithm to adjust the coded fragments assignments. Simulation results show that the performance of the proposed heuristic algorithm is close to that of the ILP, and only a small portion of nodes need to recalculate their assignments when using the proposed adjustment algorithm in the regrowing blockchains.