Threshold Selection for Iterative Decoding of (v,w)-regular Binary Codes

Iterative bit flipping decoders are an efficient and effective choice for decoding codes which admit a sparse parity-check matrix. Among these, sparse (v,w)-regular codes, which include LDPC and MDPC codes, are of particular interest both for efficient data correction and the design of cryptographic primitives. Throughout the iterative decoding process, the bit flipping thresholds can be determined either statically or during the decoder execution, by using information coming from the initial syndrome value and its updates. In this work, we analyze a two-iterations parallel hard decision bit flipping decoder and propose concrete criteria for threshold determination, backed by a closed form model. In doing so, we introduce a new tightly fitting model for the distribution of the Hamming weight of the syndrome after the first decoder iteration and substantial improvements on the decoding failure rate (DFR) estimation with respect to existing approaches.