Advancement in technology has complemented the increased complexity of state-of-the-art video coding standards by providing high-performance multimedia platforms. This has resulted in non-negligible computational reliability issues, especially with respect to soft errors. This paper motivates the dire need towards computationally Reliable Video Coding (ReVC) on modern hardware platforms. We highlight the issues with the help of a fault injection analysis during the CAVLC processing. We present a case study on error-tolerant CAVLC, where error tolerance is achieved at various levels of abstraction, ranging from algorithm to hardware. Application-specific knowledge of CAVLC is used to detect potential errors at the algorithm level, while hardware means are provided to protect the tables for CAVLC. Experiments demonstrate that our approach significantly improves the video quality under high fault rates. Furthermore, we demonstrate that when considering the application-specific knowledge, our proposed solution incurs minimal area and performance overhead compared to redundancy-based reliability methods.