Cycle-Detection Based Decimation Policies for Lossy Source Encoding

We propose a variant of the belief propagation guided decimation (BPGD) algorithm for the lossy binary sym-metric source coding problem, called DeciPolicy, which enables different decimation policies to decide when to trigger decimation, which variables to decimate, and which value to assign to decimated bits. In particular, we introduce a method that uses information about the cycles existing in the graph of a low-density generator matrix (LDGM) code to select candidate nodes for decimation. The proposed family of policies can be combined to include cycle detection-based decimation, parallel decimation of several bits, and random or hard value assignment. We demonstrate the algorithms on different constructions of LDGM codes, including an optimized irregular degree distribution and semi-regular Ising models, and show that our decimation policies lower the distortion when compared to various classical soft and hard BPGD algorithms, closing the gap to the rate-distortion limit.