Table 1 Message definitions in the factor graph

\(p_{\textsf{a1}}^{-, t}(a_{n, 1})\)

Message from \(a_{n, 1}\) to \(p(a_{n, 1})\)

\(p_{\textsf{a1}}^{+, t}(a_{n, 1})\)

Message from \(p(a_{n, 1})\) to \(a_{n, 1}\)

\(p_{\textsf{a1}}^{-, t}(a_{n, k})\)

Message from \(a_{n, k}\) to \(p(a_{n, k} | a_{n, k - 1})\), \(k \ge 2\)

\(p_{\textsf{a1}}^{+, t}(a_{n, k})\)

Message from \(p(a_{n, k} | a_{n, k - 1})\) to \(a_{n, k}\), \(k \ge 2\)

\(p_{\textsf{a2}}^{-, t}(a_{n, k})\)

Message from \(p(a_{n, k + 1} | a_{n, k})\) to \(a_{n, k}\), \(k \le K - 1\)

\(p_{\textsf{a2}}^{+, t}(a_{n, k})\)

Message from \(a_{n, k}\) to \(p(a_{n, k + 1} | a_{n, k})\), \(k \le K - 1\)

\(p_{\textsf{a3}}^{-, t}(a_{n, k})\)

Message from \(p(x_{n, k} | a_{n, k})\) to \(a_{n, k}\)

\(p_{\textsf{a3}}^{+, t}(a_{n, k})\)

Message from \(a_{n, k}\) to \(p(x_{n, k} | a_{n, k})\)

\(p_{\textsf{x}}^{-, t}(\varvec{x}_{k})\)

Message from \(\delta (\varvec{z}_{k} - \varvec{H} \varvec{x}_{k})\) to \(\varvec{x}_{k}\)

\(p_{\textsf{x}}^{+, t}(\varvec{x}_{k})\)

Message from \(\varvec{x}_{k}\) to \(\delta (\varvec{z}_{k} - \varvec{H} \varvec{x}_{k})\)

\(p_{\textsf{z}}^{-, t}(\varvec{z}_{k})\)

Message from \(p(\varvec{y}_{k} | \varvec{z}_{k})\) to \(\varvec{z}_{k}\)

\(p_{\textsf{z}}^{+, t}(\varvec{z}_{k})\)

Message from \(\delta (\varvec{z}_{k} - \varvec{H} \varvec{x}_{k})\) to \(\varvec{z}_{k}\)