Further Results on Finite-Length Analysis of BATS Codes

Abstract

BATS codes were proposed for communication through networks with packet loss. A BATS code consists of an outer code and an inner code. The outer code is a matrix generalization of a fountain code, which works with the inner code that comprises random linear coding at the intermediate network nodes. In this paper, we present some new results on the finite-length performance of BATS codes with respect to both belief propagation (BP) decoding and inactivation decoding. Our results reveal explicitly how the number of batches used for decoding affect the decoding performance for both BP decoding and inactivation decoding. We further derive i) the error exponent of BP decoding, ii) a finite summation expression of the expected number of batches consumed by BP decoding, and iii) the asymptotic behavior of the number of inactive symbols required when the number of batches used for decoding goes to infinity.