We present a new class of finite-precision decoders for low-density parity-check (LDPC) codes. These decoders are much lower in complexity compared to conventional floating-point decoders such as the belief propagation (BP) decoder, but they have the potential to outperform BP. The messages utilized by the decoders assume values (or levels) from a finite discrete set. We discuss the implementation aspects as well as describe the underlying philosophy in designing these decoders. We also provide results to show that in some cases, only 3 bits are required in the proposed decoders to outperform floating-point BP.
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