When considering error-correction codes for applications, the most important aspect of a coding scheme becomes the ratio of error-correction performance versus cost. This work studies the decoding of LDPC codes, and presents a new iterative decoding algorithm that represents likelihood as binary stochastic streams, but uses some elements of the sum-product algorithm in its variable node. To convert the stochastic streams to a log-likelihood ratio representation, the algorithm uses the principle of successive relaxation. Because likelihood is represented as stochastic streams, processing nodes only exchange 1 bit messages, which results in a low-complexity interleaver. Simulations show that the proposed algorithm achieves excellent error-correction performance and can outperform the floating-point sum-product algorithm. We also study the problem of error floors in LDPC codes, and the manner in which it can be addressed at the level of the decoder. After reviewing existing solutions, an alternative technique for lowering error floors is presented. The technique, called redecoding, relies on the randomized progress of a decoding algorithm to successfully decode problematic frames. Simulation of one code shows that redecoding removes the floor at least down to a bit error rate of 10-12.
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