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The backwards message is computed in a similar fashion.

Whereas the forward message is computed forwards from 1 to k, the backwards message is computed backwards from t to k + 1.

Formally, each symbol of the message is computed as m k,l =σ W (2(b k,l ⊕r k,l )−1), 0≤l≤L−1.

If the codeword is transmitted over an error-free channel, then is checked to be all-zero by (17) and the transmission message is computed by (22) as follows: (25).

Here, only two values are computed and propagated for the magnitude of c2v messages; specifically, if we define (2). the index of the smallest variable-to-check (v2c) message entering CN, then a dedicated c2v message is computed in response to VN : (3).

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Let a probable EIRP range, for this message be computed as set forth in Heuristic 1.

end{aligned} (9 Other messages are computed accordingly.

Specific messages are computed and passed along each edge of the graph.

In a nutshell, the factor graph is divided into two parts, the BP part and the MF part, where, respectively, BP-like and MF-like messages are computed.

Once these messages are computed, the smoothing distribution can be computed easily by multiplying the forward and backward messages as p ( Ψ τ | x 1 : F, 1 : T ) ∝ α τ , (42).

V-A can be removed if the v2c messages are computed twice on-the-fly, as shown in Figure 8: the first time to feed the array of CNUs, and then to update the SOs.

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