Techniques of this disclosure provide an indication of whether performing random access from a particular access unit in a bitstream requires fetching of parameter sets from previous access units. A clean random access (CRA) picture can be positioned at any point within a coded video sequence and does not clean a decoded picture buffer (DPB) of a video decoder. In order to perform random access decoding from the CRA picture, a video decoder may need to fetch one or more parameter sets included in unavailable access units that precede the CRA picture. The techniques provide an indication, for each CRA picture, that indicates whether parameter sets included in previous access units are needed to perform random access from the picture. When no parameter sets from previous access units are needed for random access from a particular CRA picture, a video decoder may determine to perform random access from that picture.