# Psychaocoustic Models for Perceptual Audio Coding--A Tutorial Review
## 3 Coding of Stereo Signals
### Models for Coding of Stereo Signals  
When coding a stereo pair of audio channels, audio coders attempt to take advantage of possible redundancy or irrelevance between the two channel signals. To this end, techniques for _joint stereo coding_ are employed [15; 44], which jointly process the two channel signals in their spectral representations. While there are different approaches for joint processing, in many cases the use of joint stereo processing leads to further extensions of the coder's psychoacoustic model for:  
* adaptation of the coding thresholds (i.e., thresholds used for controlling the codec's quantization noise) to fit to the joint stereo processing, if used;
* on/off control of the joint stereo processing. Therefore, in an encoder with joint stereo processing (see Figure 6), the joint stereo encoding is controlled by the perceptual model and the coding thresholds are adapted according to the joint stereo coding. The control information for the joint stereo processing is multiplexed as side information into the bitstream. This side information is used in the decoder (see Figure 7) to control the joint stereo decoder processing. Figure 5: Illustration of different binaural sound propagation to the ears. (**a**) Propagation path length difference; (**b**) direct and diffuse sound due to wall reflection. The most widely known and simple scheme for joint stereo coding is Mid/Side (M/S) stereo coding, which encodes the sum and the difference between left and right channel signal rather than the original signals [45, 46]. The primary benefits of M/S stereo coding can be described by two factors:  
* Spatial unmasking prevention: Since independent coding of channel signals introduces uncorrelated quantization noise signals into both channels, masking of this noise by the music signal may be significantly reduced due to spatial unmasking by the BMLD effect. This is especially severe for near-monophonic signals where the spatial image of the signal is perceived in the center of the sound stage, whereas the noise is spread out to the far left and right [44]. In such cases, the activation of M/S stereo helps to put the coding noise \"behind\" the masker signal into the center of the sound stage, and thus prevent BMLD-induced unmasking. * Bitrate saving: For near-monophonic signals, significant savings in bitrate can be achieved as compared to independent coding of the channel signals. Thus, for using M/S stereo, the psychoacoustic model of the codec has to be extended in two ways:
* Adaptation of coding thresholds: When M/S stereo coding is activated in a codec, the quantization noise signals of the two coding channels pass through a sum-difference matrix before being presented to the listener as left and right channel output signals. As a consequence, the same amount of noise contribution is present in both output channels (independent control over noise levels is no longer possible) and the noise contributions appear at the output as correlated (M channel) and anti-correlated (S channel) rather than uncorrelated from each other, leading to different BMLD conditions. Thus, the coding thresholds have to be modified for M/S processing to ensure that all monaural and spatial masking conditions are met properly at the codec's output. One approach is to calculate suitable thresholds using explicit models for BMLD effects, as has been described in previous studies [2, 17, 46]. A second, more simplistic approach to threshold calculation has been described in another study [44], where the consideration of meeting individual target thresholds that ensure proper monophonic masking at the channel outputs leads to a common coding threshold for M and S channels as the _minimum of the monophonic L and R channel  
Figure 6: Encoder with Joint Stereo Processing. Figure 7: Decoder with Joint Stereo Processing. thresholds in each frequency band_ to consider the worst-case for each individual output channel.