Rate Distortion Bounds for Binary Erasure Source Using Sparse Graph Codes

We consider lower bounds on the rate-distortion performance for the binary erasure source(BES) introduced by Martinian and Yedidia, using sparse graph codes for compression. Our approach follows that of Kudekar and Urbanke, where lower bounds on the rate distortion performance of low-density generator matrix (LDGM) codes for the binary symmetric source(BSS) are derived. They introduced two methods for deriving lower bounds, namely the counting method and the test channel method. Based on numerical results they observed that the two methods lead to the same bound. We generalize these two methods for the BES and prove that indeed both methods lead to identical rate-distortion bounds for the BES and hence, also forthe BSS.