One and Two Bit Message Passing for SC-LDPC Codes with Higher-Order Modulation
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High throughput and low complexity decoding algorithms are necessary in optical communications to meet the targeted data rate requirements. A new quaternary message passing (QMP) algorithm for belief propagation decoding of low-density parity-check (LDPC) codes is proposed and analyzed asymptotically by density evolution. At the variable nodes soft information from the channel output is exploited, but each message is represented by two bits only during the iterative information exchange between variable and check nodes. Hereby, the internal data flow in the decoder is decreased. QMP is compared asymptotically and in finite length simulations to binary message passing (BMP) and ternary message passing (TMP) for spectrally efficient communication with higher-order modulation and probabilistic amplitude shaping (PAS). To showcase the potential of quantized message passing decoders for high throughput forward error correction, a scenario with spatially coupled LDPC codes and a target spectral efficiency of 3.0 bits/QAM symbol is considered. Gains of up 0.7 dB and 0.1 dB are observed compared to BMP and TMP, respectively. The gap to unquantized belief propagation decoding is reduced to about 0.75 dB.
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