Zigzag code

Zigzag code is a simple linear error-correcting code [ Li Ping, "Zigzag codes and concatenated zigzag codes", IEEE Trans. Inform. Theory, special issue on codes on graphs, vol., IT-47, no. 2, pp., 800–807, Feb. 2001.] . It can be described graphically as it is shown on the picture. Green nodes $d(i,j)$ represent data bits (information to be encoded). Yellow circles $p(i)$ are the parity bits. For example $p(1)\; =\; d(1,1)oplus\; d(1,2)\; oplus\; d(1,3)$, where $oplus$ denotes modulo-2 addition.