Stochastic decoding is a new alternative approach for iterative decoding on graphs. The capability of stochastic decoding has been recently validated for decoding Low-Density Parity-Check (LDPC) codes. This article extends the application of the stochastic approach to decode linear block codes with highdensity Parity-Check Matrices (PCMs) such as Bose-Chaudhuri-Hocquenghem (BCH) codes, Reed-Solomon (RS) codes and, block turbo codes based on BCH component codes. We show how the stochastic approach, despise its bit-serial nature, is able to generate soft-output information for iterative Soft-Input Soft-Output (SISO) decoding. This article describes the structure of high-degree stochastic variable nodes used in codes with high-density PCMs. Simulation results for a (128, 120) BCH code, a (31, 25) and a (63, 55) RS code and, a (256, 121) and a (1024, 676) BCH block turbo code demonstrate decoding performance close to the iterative SISO decoding with floatingpoint implementation.

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