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 information-bottleneck 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 information-bottleneck 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 message alignment 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 0.15 dB worse than a double-precision belief propagation decoder and outperforms a min-sum decoder.

Coarsely Quantized Decoding and Construction of Polar Codes Using the Information Bottleneck Method

“…The huge number of lookup tables used in the information bottleneck decoders of [26] can be viewed as a space complexity cost for their computational simplicity. We demonstrate that using the message alignment technique of [7], the required number of tables and, hence, the space complexity of the information, bottleneck SCL decoders can be reduced.…”

“…It was reported that an information bottleneck decoder having a bitwidth as low as 4 bits performs very close to the belief propagation decoder [1]. The idea of information bottleneck decoders was extended to irregular LDPC codes in [7,8]. Design of quantized message passing decoders that utilize information preserving table lookup operations was also addressed in [9][10][11][12].…”

“…Results of [1,2,7,12] encourage to explore the application of the information bottleneck method in polar codes [13], an important class of channel codes that are seen as a breakthrough in the coding theory. They are the first linear block codes that can provably achieve the symmetric capacity of binary input memoryless channels.…”

“…Hence, a polar code and its tailored quantized decoder are obtained from the same process. Similar to the information bottleneck LDPC decoders [1,7], all the operations in the information bottleneck SC decoder are table lookups of unsigned integers. However, the path metric computation in an information bottleneck SCL decoder is done similar to that in a conventional decoder as in [27].…”

Decoding of Non-Binary LDPC Codes using the Information Bottleneck Method

“…Recently, several authors considered a novel approach for decoding of binary LDPC codes [7]- [12]. In these works, a principle was applied which is fundamentally different from state-of-the-art signal processing approaches.…”