This paper presents a novel distributed video coding (DVC) scheme using compressive sensing (CS) that achieves low-complexity for encoding and efficient signal sensing. Most CS recovery algorithms rely only on signal sparsity. Yet, under DVC architecture, additional statistical characterization of the signal is available, which offers the potential for more precise CS recovery. First, a set of random measurements are acquired and transmitted to the decoder. The decoder then exploits the statistical characterization of the signal and generates the side information (SI). Finally, utilizing the SI, a Bayesian inference using belief propagation (BP) decoding is performed for signal recovery. The proposed CS-DVC system offers a more direct way of signal acquisition and the potential for more precise estimation of the signal from random measurements. Experimental results indicate that SI can improve the signal reconstruction quality in comparison with a CS recovery algorithm that relies only on the sparsity.