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Video transcoding is a process that converts video from one compressed format to another one of different bit-rate, temporal and/or spatial resolution. It is one of the enabling technologies for the universal multimedia access in heterogeneous environment of communication networks and network access devices. The goal of the transcoding research is to aim at the best possible quality-complexity trade-off under given application constraints by utilizing statistics from the input compressed video. In this dissertation, we propose new algorithms to improve the transcoding performance in terms of quality-complexity trade-off. First, we present new motion re-estimation (MRE) algorithms for spatial and temporal transcoding. Existing relationship between the pixels of a frame and its reference frame(s) via input motion vectors (MVs) is used to derive the MVs required to code the output video. We also propose a simple adaptive re nement method that selectively reones the target MVs in small vicinity. Experimental results using the cascaded pixel-domain transcoder (CPDT) show performance gain over the known existing methods; this performance is comparable with the full scale motion estimation (FSME). The proposed MRE algorithms are then extended to address rate-distortion optimized motion estimation and mode decision, which is called RDO, with variety of inter prediction modes and multiple reference frames in H.264 standard. We also present fast mode decision methods that use low-complexity coding rate calculations based on domain model. Experimental results show comparable performance with RDO at much reduced cost. Next, we present a new rate control algorithm for H.264 transcoding that estimates important parameters, namely the mean absolute differences (MAD), picture complexity, and header and MV bits used in rate-distortion model, adopted in H.264, for the current picture from their values at input picture and previous output picture(s) of the transcoder. Experimental results show improved quality and scene-change handling capability.