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Linear programming (LP) decoding of low-density parity-check codes over discrete memoryless symmetric channels was introduced by Feldman et al. Here, we extend the LP decoding paradigm by applying it to two additional scenarios: joint source-channel (JSC) coding and decoding over the infinite-memory non-ergodic binary Polya-contagion channel. Simulation results indicate that the JSC LP decoder yields significant gains over the standard LP decoder for non-uniform sources. Simulations also show that the LP decoder for the Polya channel performs moderately well in relation to the epsiv-capacity limit.