Impact of Stopping Set Properties on Iterative Decoding of FG-LDPC Codes on the Binary Symmetric Channel

Stopping set properties determine the iterative decoding performance of any linear block code on the Binary Erasure Channel (BEC). Furthermore, there is a common conception that they are crucial factors on other channels, like the Binary Symmetric Channel (BSC), as well. In order to investigate whether this is true indeed, we study stopping set properties and iterative decoding performance on the BSC of Finite-Geometry Low-Density Parity-Check (FG-LDPC) codes, which have been chosen due to their effectiveness and the good structure of their parity-check matrices (PCMs). Also modified versions of these PCMs are considered. As a rather surprising result, we show that a PCM with better stopping set properties than another PCM of the same code does not necessarily lead a better decoding performance on the BSC. Also, PCMs of the same code with the same stopping set properties, do not always have the same decoding performance on the BSC.