Analysis of Bit-Flipping Algorithm of Irregular Low-Density Parity-Check Codes

Abstract

In this work, we analytically derive the evolution of single-bit messages in the bit-flipping algorithm (BFA) for irregular low-density parity-check (LDPC) codes on the binary symmetric channel (BSC). In particular, the analysis tracks the probability distributions of the flipping functions and the bit-decision error at each iteration, which is possible by introducing a state variable at each variable node. The probability distributions are indirectly obtained by taking advantage of the state and state transition probabilities. The analysis will be confirmed by comparing analytic evaluations with simulation results. For the comparison, we implement LDPC codes at a finite length.