VIDEO ENCODING APPARATUS, VIDEO DECODING APPARATUS, VIDEO ENCODING METHOD, AND VIDEO DECODING METHOD FIELD The embodiments discussed herein are related to a video encoding apparatus and video encoding method that can edit encoded video data without decoding the video data, and also relates to a video decoding apparatus and video decoding method for decoding video data encoded by such a video encoding apparatus. BACKGROUND Generally, the amount of data used to represent video data is very large. Accordingly, an apparatus handling such video data compresses the video data by encoding before transmitting the video data to another apparatus or before storing the video data in a storage device. Coding standards such as MPEG-2 (Moving Picture Experts Group Phase 2), MPEG-4, and H.264 MPEG-4 Advanced Video Coding (MPEG-4 AVC/H.264), devised by the International Standardization Organization/International Electrotechnical Commission (ISO/IEC), are typical video coding standards widely used today. Such coding standards employ an inter-coding method that encodes a picture by using not only information from itself but also information from pictures before and after it, and an intra-coding method that encodes a picture by using only information contained in the picture to be encoded. The inter-coding method uses three types of pictures, referred to as the intra-coded picture (I picture), the forward predicted picture (P picture) which is usually predicted from a past picture, and the bidirectional predicted picture (B picture) which is usually predicted from both past and future pictures. Generally, the amount of code of a picture or block encoded by inter-coding is smaller than the amount of code of a picture or block encoded by intra-coding. In this way, the amount of code varies from picture to picture within the same video sequence, depending on the coding mode selected. Similarly, the amount of code varies from block to block within the same picture, depending on the coding mode selected. Therefore, in order to enable a data stream containing encoded video to be transmitted at a constant transmission rate even if the amount of code temporally varies, a transmit buffer for buffering the data stream is provided at the transmitting end, and a receive buffer for buffering the data stream is provided at the receiving end. MPEG-2 and MPEG-4 AVC/H.264 each define the behavior of a receive buffer in an idealized video decoding apparatus referred to as the video buffering verifier (VBV) or the coded picture buffer (CPB), respectively. For convenience, the idealized video decoding apparatus will hereinafter be referred to simply as the idealized decoder. It is specified that the idealized decoder performs instantaneous decoding that takes zero time to decode. For example, Japanese Laid-open Patent Publication No. 2003-179938 discloses a video encoder control method concerning the VBV. In order for the receive buffer in the idealized decoder to not overflow or underflow, the video encoder controls the amount of code to guarantee that all the data needed to decode a given picture are available in the receive buffer when the idealized decoder decodes that given picture. When the video encoder is transmitting an encoded video data stream at a constant transmission rate, the receive buffer may underflow if the transmission of the data needed to decode the picture has not been completed by the time the picture is to be decoded and displayed by the video decoder. In other words, the receive buffer underflow refers to a situation in which the data needed to decode the picture are not available in the receive buffer of the video decoder. If this happens, the video decoder is unable to perform decoding, and frame skippir occurs. In view of this, the video decoder displays the picture after delaying the stream by a prescribed time from its receive time so that the decoding can be done without causing the receive buffer to underflow. As described earlier, it is specified that the idealized decoder accomplishes decoding in zero time. As a result if the input time of the i-th picture to the video encoder is t(i), and the decode time of the i-th picture at the idealized decoder is tr(i), then the earliest tin, at which the picture becomes ready for display is the same as tr(i). Since the picture display period (t(i+l) - t