Loop removal from LDPC codes

It is hypothesised that small loops in the graphical representations of low-density parity-check codes are detrimental to the code's performance. We demonstrate a procedure for removing such loops from the codes. An algorithm based on the code's adjacency matrix is used to locate unwanted loops, and then certain edges within the graph are exchanged to eliminate those loops (without simultaneously creating any others). This process can be repeated until there are no loops remaining with a size less than a particular limit. A comparison of some theoretical and experimental values for this limit is given.