Graph-based codes allow us to visualize error-correcting codes and construct systems of low-complexity decoding. However, certain roadblocks- called stopping sets- can prevent complete error correction. This raises a question: how can we design encoding strategies that avoid such roadblocks? We investigate a setting where we must look at partitions of variable nodes with the goal of avoiding stopping sets in at least one part. Specifically, we examine an example with six variable nodes in a Tanner graph and its corresponding 4X6 parity-check matrix. We present a proof for the partial error correction for two out of three parts in the partition. Looking forward, we aim to determine the probability of encountering stopping sets in a topological lifting of the graph.
