Information-Bottleneck Decoding of High-Rate Irregular LDPC Codes for Optical Communication Using Message Alignment

Abstract

In high-throughput applications, low-complexity and low-latency channel decoders are inevitable. Hence, for low-density parity-check (LDPC) codes, message passing decoding has to be implemented with coarse quantization—that is, the exchanged beliefs are quantized with a small number of bits. This can result in a significant performance degradation with respect to decoding with high-precision messages. Recently, so-called <i>information-bottleneck</i> decoders were proposed which leverage a machine learning framework (i.e., the information bottleneck method) to design coarse-precision decoders with error-correction performance close to high-precision belief-propagation decoding. In these decoders, all conventional arithmetic operations are replaced by look-up operations. Irregular LDPC codes for next-generation fiber optical communication systems are characterized by high code rates and large maximum node degrees. Consequently, the implementation complexity is mainly influenced by the memory required to store the look-up tables. In this paper, we show that the complexity of <i>information-bottleneck</i> decoders remains manageable for irregular LDPC codes if our proposed construction approach is deployed. Furthermore, we reveal that in order to design information bottleneck decoders for arbitrary degree distributions, an intermediate construction step which we call <i>message alignment</i> has to be included. Exemplary numerical simulations show that incorporating message alignment in the construction yields a 4-bit information bottleneck decoder which performs only <inline-formula> <math display="inline"> <semantics> <mrow> <mn>0.15</mn> </mrow> </semantics> </math> </inline-formula> dB worse than a double-precision belief propagation decoder and outperforms a min-sum decoder.