Batched Sparse Codes

TL;DR: This paper introduces batched sparse code (BATS code), which enables a digital fountain approach to resolve the above issue of high computational and storage costs in the network devices and terminals.

Abstract: Network coding can significantly improve the transmission rate of communication networks with packet loss compared with routing. However, using network coding usually incurs high computational and storage costs in the network devices and terminals. For example, some network coding schemes require the computational and/or storage capacities of an intermediate network node to increase linearly with the number of packets for transmission, making such schemes difficult to be implemented in a router-like device that has only constant computational and storage capacities. In this paper, we introduce batched sparse code (BATS code), which enables a digital fountain approach to resolve the above issue. BATS code is a coding scheme that consists of an outer code and inner code. The outer code is a matrix generation of a fountain code. It works with the inner code that comprises random linear coding at the intermediate network nodes. BATS codes preserve such desirable properties of fountain codes as ratelessness and low encoding/decoding complexity. The computational and storage capacities of the intermediate network nodes required for applying BATS codes are independent of the number of packets for transmission. Almost capacity-achieving BATS code schemes are devised for unicast networks and certain multicast networks. For general multicast networks, under different optimization criteria, guaranteed decoding rates for the destination nodes can be obtained.