Fig. 1

General system model of distributed linear block codes. It requires two time slots to complete the whole communication transmission, where solid and dashed lines denote the first and second time slots, respectively. The source and relay nodes have linear block codes \(C_1\) and \(C_2\), respectively, which are distributed to achieve coded cooperation. The resulted code at the destination is \(C=\{|\textbf{c}_1 |\textbf{c}_2 |,\textbf{c}_1\in C_1,\textbf{c} _2\in C_2\}\). Since no additional information is generated at the relay (the information at the relay depends on the information at the source) in our proposed system model, the code C is a subcode of \(\bar{C}=\{|\textbf{c}_1 |\bar{\textbf{c}}_2 |,\textbf{c}_1 \in C_1,\bar{\textbf{c}} _2\in C_2\}\), where \(\bar{\textbf{c}} _2\) corresponds to the information independent on the information at the source