The lossy compression produces smaller compression files compared to existing lossless methods. The lossless compression is used to assure the high accuracy of data.
I am not sure what you mean by "Advanced Coding Mode".
Lossless compression means that the decoder can reconstruct the original data exactly. This is a much stronger requirement than "high accuracy". For example, if your original signal contains noise, lossless coding will enable you to reconstruct the noise exactly as it was in the original, while high accuracy coding may cause the reconstructed noise to be somewhat different from the original noise.
You may consider lossless coding algorithms as a subset of the lossy coding algorithms, characterized by a reconstruction error of 0. Suppose you specify your accuracy and compression ratio requirements and then look for the lowest complexity algorithm that meets those requirements. Clearly the optimal solution that you will find in the larger set of lossy coding algorithms will be at least as good as the optimal solution that you will find in the subset of lossless solutions.
Most audio and video compression schemes contain both lossless and lossy processing stages. Sometimes the lossless stages are the most computationally intensive ones. For example in MPEG video compression there may be an arithmetic coding stage which is lossless but computationally intensive. It depends on the specific coder you consider and how much compression you attempt to achieve.
Another factor is the processing hardware you are using. The same algorithm may have very different complexities when implemented on a general purpose CPU, a DSP or graphic processing unit (GPU).
Regard to quality metric in standard coding, PSNR is still heavily used in the video compression. Recently, SSIM has been adopted as additional quality measure.
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