Existing encoder rate control (ERC) solutions have two technical limitations that prevent them from being widely used in real-world applications. One is that encoder side information (ESI) is required to be generated which increases the complexity at the encoder. The other is that rate estimation is performed at bit plane level which incurs computation overheads and latency when many bit planes exist. To achieve a low-complexity encoder, we propose a new ERC solution that combines an efficient encoder block mode decision (EBMD) for the distributed residual video coding (DRVC). The main contributions of this paper are as follows: 1) ESI is not required as our ERC is based on the analysis of the statistical characteristics of the decoder side information (DSI); 2) a simple EBMD is introduced which only employs the values of residual pixels at the encoder to classify blocks into Intra mode, Skip mode, and WZ mode; 3) an ERC solution using pseudo-random sequence scrambling is proposed to estimate rates for all WZ blocks at frame level instead of at bit plane level, i.e., only one rate is estimated; and 4) a quantization-index estimation algorithm (QIEA) is proposed to solve the problem of rate underestimation. The simulation results show that the proposed solution is not only low complex but also efficient in both the block mode decision and the rate estimation. Also, as compared to DISCOVER system and the state-of-the-art ERC solution, our solution demonstrates a competitive rate-distortion(RD)performance. Due to maintain the low-complexity nature of the encoder and have good RD performance, we believe that our ERC solution is promising in practice.