Algorithm 1 Example real-time global iteration scheduling scheme.

1:Input: Received signal $r\left(t\right)$ belonging to the k-th LDPC code word in a transmitted sequence.   2:Assumptions: k is the master time (sequence) index, $b_{\alpha }$ indicates an inactive buffer, $\beta$-mode is defined.   3:Initialization: Increment k, activate $B\left[b_{\alpha }\right]$, and set ${\mathit{It}}_{\mathrm{cur}}=0$. Perform the $\alpha$-iteration and possibly one $\beta$-iteration per active buffer:   4: for  $b=0,1,\dots ,N_{\mathrm{buf}}-1$  do   5:      if $B\left[b\right]$ is Active then   6:              Increment $B\left[b\right]$’s latency counter;   7:            if $b==b_{\alpha }$ then   8:               Perform the $\alpha$-iteration using $r\left(t\right)$ and filling $B\left[b\right]$;   9:               Increment ${\mathit{It}}_{\mathrm{cur}}$;  increment $B\left[b\right]$’s iteration counter;  deactivate $B\left[b\right]$ if parity check passes; 10:            else if $\beta$-mode == TRUE then 11:               Perform a $\beta$-iteration drawing from $B\left[b\right]$ and updating $B\left[b\right]$; 12:               Increment ${\mathit{It}}_{\mathrm{cur}}$;  increment $B\left[b\right]$’s iteration counter;  deactivate $B\left[b\right]$ if parity check passes; 13:            end if 14:      end if 15: end for Allocate Remaining $\beta$-Iterations to Oldest Buffer: 16:for $i={\mathit{It}}_{\mathrm{cur}},\dots ,{\mathit{It}}_{\mathrm{bgt}}-1$ do 17:      Identify $b_{\max }$; 18:      if $b_{\max }==-1$ then 19:            Stop iterations; 20:      else 21:            Perform a $\beta$-iteration using $B\left[b_{\max }\right]$; 22:            Increment ${\mathit{It}}_{\mathrm{cur}}$;  increment $B\left[b_{\max }\right]$’s iteration counter;  deactivate $B\left[b_{\max }\right]$ if parity check passes; 23:      end if 24: end for Ensure at Least One Buffer is Available for Next Time: 25:Identify $C_{\max }$, $b_{\max }$, and $b_{\mathrm{inactive}}$; 26:if $C_{\max }==L_{\max }$ then 27:      Declare a decoder failure; 28:      Deactivate $B\left[b_{\max }\right]$; 29:      Set $b_{\alpha }=b_{\max }$; 30: else 31:      Set $b_{\alpha }=b_{\mathrm{inactive}}$; 32: end if 33:Output $\widehat{\mathbf{y}}[k-L_{\max }+1]$, which was filled somewhere above when its buffer was deactivated;