In this paper, we study the theoretical problem of the end-to-end rate assignment for multi-hop wireless networks. Specifically, we consider the problem of joint congestion control, random access and power control design with multi-hop transmissions and interference-limited link rates. In order to address both the end-to-end throughput maximization and energy efficiency, we formulate this problem into a cross-layer design problem under a realistic interference-based communication model, which captures the attainable link capacity in practice. There are primarily three challenges in this design: 1) how to formulate the cross-layer design; 2) how to solve the non- convex and non-separable problem efficiently; more importantly 3) under a reasonably complexity, how to design a distributed algorithm that can realize this formulation while maintaining the architectural modularity among different layers. First, we propose a novel method that can convert a non- convex and non-separable programming into an equivalent convex programming problem. The problem is solved by a dual decomposition technique. We show that the resulting algorithm can be practically realized. We then design a distributed algorithm that jointly considers random access and power control to adapt for the transport layer congestion status. Simulation results confirm that the proposed algorithm can achieve close to the global optimum within reasonable convergence times.