Investigation of simple threshold shifting for bit-flip decoding

Remarkably low error rates can be obtained using low-density parity-check (LDPC) codes and their use is now an increasingly common option in communications standards. The classic decoders based on belief propagation offer very high performance but have high implementation complexity. Therefore over the last decade simpler architectures such as the bit flipping class of algorithms have been researched. Recently, a number of adaptive threshold algorithms have been proposed in which at each iteration a bit is either flipped if it is below an inversion threshold, or the threshold is lowered. By choosing certain values of the scaling factor, the scaling can be efficiently implemented using a small number of shift and add operations. This work looks at how the scaling factor affects the convergence and error performance, and investigates an algorithm that switches between two scaling values based on the syndrome sum. The dual scaling method maintained the error performance compared to that with a single scaling but the iteration count was significantly reduced.