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The authors consider the Binary Erasure Source (BES) introduced by Martinian and Yedidia. Based on the technique introduced by Martinian and Wainwright, they upper bound the rate-distortion performance of the check regular Poisson LDGM ensemble and the compound LDGM-LDPC ensemble for the BES. They also show that there exist compound LDGM-LDPC codes, with degrees independent of block-length, which can achieve any given point on the Shannon rate-distortion curve of the BES. Following the remarkable success of sparse graph codes for the channel coding problem, many researchers have explored their capabilities for various source coding problems. One of the first contributions in this direction was made, where Martinian and Yedidia introduced the Binary Erasure Source (BES).
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