A redundant data transmission system with linear topology is studied using reliability modeling of a heterogeneous hot standby system with one repair unit and exponential repair time of its failed elements (data transmission channels). Two cases are considered - a special one, when the lifetime distribution of the elements is exponential, and a generalized one, when their lifetimes have general independent distribution. The goal of this paper is to calculate the reliability characteristics of the system and to investigate the effect of cross-redundancy on the system-level reliability.