Applications for providing services via the Internet (e.g., video-conference, digital video broadcast, and Video on Demand services including video content streaming) are increasing.  These applications rely on transmission of video data.  When the applications transmit video data, most video data is transmitted via a conventional transmission path having a limited bandwidth.  Furthermore, when the applications record video data, most video data is recorded on a conventional recording medium having a limited capacity.  To transmit video data via the conventional transmission path or record video data on the conventional recording medium, it is indispensable to compress or reduce the data amount of the video data. 
In view of this, many video coding standards have been developed to compress video data.  These video coding standards are, for example, ITU-T standards denoted as H.26x and ISO/IEC standards denoted as MPEG-x. Currently, the latest and most advanced video coding standard is the standard denoted as H.264/MPEG-4 AVC (see Non Patent Literature 1 and Non Patent Literature 2). 
The coding approach underlying most of these video coding standards is based on prediction coding that includes the following main steps of (a) to (d): (a) Divide each video frame into blocks each having pixels to compress data of the video frame on a block-by-block basis. ( b) Predict each block based on previously coded video data to identify temporal and spatial redundancy. ( c) Subtract the predicted data from the video data to remove the identified redundancy. ( d) Compress remaining data (residual blocks) by Fourier transform, quantization, and entropy coding. 
As for the step (a), the current video coding standard provides different prediction modes depending on a macroblock to be predicted.  According to most of the video coding standards, motion estimation and motion compensation are used for predicting video data based on a previously coded and decoded frame (inter frame prediction).  Alternatively, block data may be extrapolated from an adjacent block of the same frame (intra frame prediction). 
In the step (d), quantized coefficients included in a current block to be coded are scanned in a predetermined order (scan order).  Then, information (SignificantFlag) indicating whether the scanned coefficients are zero coefficients or non-zero coefficients (e.g., binary information (symbol) indicating a non-zero coefficient as 1 and a zero coefficient as 0) is coded. 
Furthermore, information (last position information) indicating the position of the last non-zero coefficient in the scan order is binarized, arithmetically coded, and arithmetically decoded.