Definition: Serial decoder-module class

A node may use the batch programme $U$, or the streaming programme of Theorem thm:streamupper. For an internal node:

1. child subprogrammes execute serially in order $1,2,3$;

2. a completed child returns one intermediate quantum qubit to its parent, retained in the same laboratory;

3. a parent may consume its first two intermediate qubits using its early two-input streaming stage;

4. the parent performs its final one-input stage only after child 3 has completed;

5. subprogrammes are not otherwise interleaved, and no intermediate quantum output is exported.

All child syndrome outcomes may be forgotten after their corrections. Parent record bits are retained until the parent correction.