Rate Distortion Bounds for Binary Erasure Source Using Sparse Graph Codes

Abstract

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. Ourapproach follows that of Kudekar and Urbanke, where lower bounds on the rate distortionperformance 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 countingmethod and the test channel method. Based on numerical results they observed that the twomethods lead to the same bound. We generalize these two methods for the BES and prove thatindeed both methods lead to identical rate-distortion bounds for the BES and hence, also forthe BSS.