# A High Efficiency Multistage Coder for Lossless Audio Compression using OLS+ and CDCCR Method
## 10 Conclusions  
This work presents an extended version of the cascading audio data encoder. In classic solutions of lossless audio coding, adaptive versions of Rice and arithmetic encoders are used interchangeably. The proposed solution uses an adaptive Golomb code, which is a generalised form of the Rice code with potentially higher compression efficiency because of a better adaptation of the code to the current probability distribution of the currently encoding data. The Golomb codec output is additionally compressed using a context-dependent adaptive binary arithmetic encoder. In contrast to CABAC [45], where the Exp-Golomb distribution is used, our proposition adapts better to the sequence of prediction errors characterised by the geometric distribution. The proposed adaptive arithmetic coder presented in this paper offers less computational complexity compared to the coder used in the work [16]. A higher degree of compression was obtained due to a better algorithm for selection of context numbers, and also due to the omission a multivalued arithmetic coder in favour a binary variant (this allows increasing the dynamics adaptation to probability distributions of individual bits of values \(u_{G}\) and \(v_{G}\) calculated in the Golomb encoder block). This solution is more flexible also in comparison to classic solutions using the adaptive Rice code. In the proposed solution, the increase in efficiency of compression compared to the most efficient option MP4-ALS-RM23 (working in backward adaptation mode) was possible due to introducing a more efficient OLS+ block in place of RLS, adding an additional CDCCR block in the cascaded predictive model and introducing an efficient CABAC based on initial compression using the adaptive Golomb code. The introduced improvements entail a disproportionately large increase in the implementation complexity relative to the reference version, for which was adopted MP4-ALS-RM23 in the best mode. Despite the increasing implementation complexity it has been kept at a level enabling real-time encoding and decoding. Similar conclusions can also be drawn by comparing the reference version (the best mode) with the MP4-ALS-RM23 in default mode. Therefore, one should be aware that shortening the length of the result files for each subsequent percentage is paid by the increasing costs of increasing the implementation complexity. This is similar to the nonlinear increase in energy necessary to speed up objects that want to approach the speed of light in vacuo. The complexity of an efficient cascade prediction system also is possible to reduce by regulation not only by modifying the orders of predictive models in NLMS blocks. We propose using the ALCM+ block with a much lower implementation complexity compared to RLS and OLS+ blocks. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**File**} & **Shorten** & \multirow{2}{*}{**TTA v3.4.1**} & \multirow{2}{*}{**MP4 1**} & \multirow{2}{*}{**FLAC v1.3.2**} & **WavPack** & **Nanozip** \\  & & & & & **v4.60.1** & **v0.09a** \\ \hline FloorEssence & 11.464 & 10.176 & 10.202 & 10.174 & 9.922 & 9.677 \\ \hline ItCouldBeSweet & 11.587 & 9.186 & 9.016 & 9.004 & 8.858 & 8.776 \\ \hline Layla & 10.871 & 10.300 & 10.377 & 10.344 & 10.202 & 9.859 \\ \hline LifeShatters & 12.177 & 11.145 & 11.182 & 11.146 & 11.052 & 10.927 \\ \hline macabre & 10.564 & 10.062 & 9.965 & 9.895 & 9.928 & 9.267 \\ \hline MaleSpeech & 7.532 & 5.530 & 5.590 & 5.649 & 5.333 & 5.024 \\ \hline SinceAlways & 12.192 & 11.243 & 11.164 & 11.211 & 10.749 & 10.564 \\ \hline thear1 & 12.574 & 11.703 & 11.742 & 11.746 & 11.635 & 11.685 \\ \hline TomsDiner & 9.709 & 8.561 & 8.534 & 8.404 & 8.087 & 7.480 \\ \hline velvet & 11.067 & 11.464 & 10.672 & 10.679 & 10.843 & 10.656 \\ \hline
**Bit average** & **10.434** & **9.421** & **9.352** & **9.331** & **9.208** & **8.881** \\ \hline \hline \end{tabular} \({}^{1}\) MP4-ALS-RM23 in default mode.  
\end{table} 
Table 5: _Cont._  
**Author Contributions:** Conceptualisation, G.U. and C.W. ; methodology, G.U.