## 4 Performance Analysis in the Absence of Non-Idealities  
### Iterative Joint Channel Decoding at the AP  
As described in Section 2., the information sequences are separately encoded using the same channel code (either an LDPC code or a SCCC) and transmitted over the communication links. In all cases, we assume that the common coding rate at the sources is \(r=L/N=1/2\). The proposed iterative decoding scheme at the AP is shown in Figure 4, where a channel decoder per source is considered and the trajectory of the iterative decoding process among the \(n\) component decoders is highlighted. The \(i\)-th component decoder, denoted as \({\rm DEC}_{i}\) (\(i=1,\ldots,n\)), receives both the channel logarithmic likelihood ratios (LLRs) and the a priori probabilities obtained by properly processing the soft-output reliability values generated by the other component decoders. This processing/combining operation is carried out in the central block, denoted as \"COMB,\" where perfect knowledge of the source correlation (i.e., \(\rho\)) is assumed. At each component subdecoder, each coded sequence is decoded by using classical decoding algorithms; for instance, in the presence of an LDPC code the classical sum-product (SP) algorithm [28]is used, whereas in the presence of a SCCC turbo decoding, based on the use of the BCJR algorithm [29], is considered [30]. Under the assumption of perfect channel state information at the receiver, the channel LLR, relative to the \(i\)-th observable (\(i\in\{1,\ldots,N\}\)) from the \(k\)-the node (\(k\in\{1,\ldots,n\}\)), can be expressed as  
\[\mathcal{L}_{i,\mathrm{ch}}^{(k)}=\ln\frac{p(r_{i}^{(k)}|y_{i}^{(k)}=1,\alpha_{ i}^{(k)})}{p(r_{i}^{(k)}|y_{i}^{(k)}=-1,\alpha_{i}^{(k)})}=\frac{2r_{i}^{(k)} \sqrt{E_{c}^{(k)}}\left|\alpha_{i}^{(k)}\right|}{\sigma^{2}} \tag{21}\]  
where \(\sigma^{2}=N_{0}/2\). The maximum number of _internal_ decoding iterations in each component decoder is denoted as \(n_{\mathrm{it}}^{\mathrm{int-max}}\), and depends on the chosen channel coding (and decoding) scheme (e.g., see note 3). The a priori information about the correlation between the sources is exploited through an _external_ iterative decoding process between the component subdecoders, and this process stops when a maximum number of external iterations (denoted as \(n_{\mathrm{it}}^{\mathrm{ext}}\)) is reached. The total LLR relative to the \(i\)-th observable at the input of the \(k\)-th subdecoder can be expressed as follows:  
\[\mathcal{L}_{i,\mathrm{in}}^{(k)}=\left\{ \begin{array}{ll}\mathcal{L}_{i, \mathrm{ch}}^{(k)}+\mathcal{L}_{i,\mathrm{ap}}^{(k)}&i=0,\ldots,L-1\\ \mathcal{L}_{i,\mathrm{ch}}^{(k)}&i=L,\ldots,N-1\end{array} \right.\]  
In other words, the LLR of the \(i\)-th observable associated with an information bit (\(i=0,\ldots,L-1\)) includes, besides the channel reliability value given by (21), the \"suggestion\" (represented by the soft reliability value \(\mathcal{L}_{i,\mathrm{ap}}^{(k)}\)) obtained from a posteriori reliability values output by the other decoders. In particular, the a priori component of the LLR at the input of the \(k\)-th decoder can be written as  
\[\mathcal{L}_{i,\mathrm{ap}}^{(k)}=\ln\frac{P(y_{i}^{(k)}=1)}{P(y_{i}^{(k)}=-1 )}\hskip 28.452756 pti=0,\ldots,L-1\]  
Figure 4: Iterative JCD scheme at the AP in the presence of \(n\) sources. where \(\{P(y_{i}^{(k)}=+1),P(y_{i}^{(k)}=-1)\}\) are derived from the soft-output values generated by the other decoders, as follows.