Transform Coefficient Level Coding in HEVC

The compression of prediction residuals is referred to as transform coefficient level coding, block-based transformed and quantized in hybrid video coding architectures such as HEVC. It is designed for improved compression efficiency and reduced complexity by a sophisticated architecture supporting variable transform block sizes. CABAC is exclusively employed in HEVC for that purpose. Its core is a table-driven binary arithmetic coder (M-Coder). Integer-valued transform coefficient levels require therefore a decomposition into binary sequences (bin string). This process is referred to as binarization and is coupled with the context modelling stage. The latter exploits statistical dependencies resulting in improved compression efficiency.

HEVC supports square transforms ranging from 4×4 to 32×32 using a nested residual quadtree (RQT). It is the task of the transform coefficient level coding to serialize the two-dimensional residual blocks for the transmission. The serialization is realized with the help of scanning patterns specifying the processing order within a residual block. Instead of having dedicated logic for each block size, HEVC specifies a decomposition into 4×4 disjoint processing units, referred to as sub blocks. Each sub-block is processed in the same manner employing a single processing logic. A wrapper logic specifies the processing order of sub blocks. The same scanning pattern is employed for both, the sub-block processing as well as the spatial positions within a sub-block, as exemplarily shown in Figure 1.

Coding Process

The coding process involves both binarization and context modelling simultaneously. In addition to that, both modules influence each other mutually, depending on the past symbols within the current sub-block and transform block. In combination with insignificance flags, the transform coefficient level coding design enables an optimal trade-off between complexity and performance. Figure 2 summarizes the of the coding processes. The grey stages operate in regular operation mode while the white stages employ the bypass operation mode. The reason for a limitation of the absLevel > 0 and absLevel > 1 becomes clearer when the underlying processes are viewed separately.

Adaptive Binarization and Context Modeling

Bin strings of absolute levels are formed by the concatenation of three binary sequences. Each binary sequence is generated using different variable-length codes: Truncated Unary (TU), Truncated Rice (TR), and Exp-Golomb (EG) codes. The TR and the EG sequences are empty for an absolute level that is smaller than a maximum allowed value (bound) for the TU code. The EG sequence is empty for an absolute level that is smaller than the TR bound, but greater or equal than the TU bound. All bounds are adaptive within a sub-block and are reset for each sub-block. The TU bound starts with a value equal to 2. It is decreased by one after the occurrence of an absolute level greater than 2, and is further decreased by one after an occurrence of eight absolute levels greater than 1. That is the main reason for the limitation in the absLevel > 1 and absLevel > 2 stages during the coding process.

The adaptive context modelling may be summarized as the assignment of symbols having a similar probability distribution to the same context model. However, only bins of the TU sequence are transmitted in the regular coding mode using adaptive context models. It is especially crucial for the significance stage due to its proportion in the bitstream. An evaluation process involving the right- and the bottom-neighbouring sub blocks derives a context model category for the current sub-block. In contrast to that, TR and EG bins are transmitted in the bypass operation mode of the M-Coder. This is the result of the adaptively controlled binarization resulting in codewords that are close to the minimum-redundancy boundary.


  1. T. Nguyen, P. Helle, M. Winken, B. Bross, D. Marpe, H. Schwarz, and T. Wiegand, Transform Coding Techniques in HEVC, IEEE Journal of Selected Topics in Signal Processing, Vol. 7, No. 6, pp. 978-989, Dec 2013.
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