Information-Bottleneck Decoding of High-Rate Irregular LDPC Codes for Optical Communication Using Message Alignment  
[PERSON]  
1 Institute of Communications, Hamburg University of Technology, 21073 Hamburg, Germany;  
[EMAIL_ADDRESS] (J.L. ); [EMAIL_ADDRESS] (G.B.) [PERSON]  
1 Institute of Communications, Hamburg University of Technology, 21073 Hamburg, Germany;  
[EMAIL_ADDRESS] (J.L. ); [EMAIL_ADDRESS] (G.B.) Footnote 1: email: {}  
Footnote 2: email: {}  
Footnote 3: email: {}  
Footnote 4: email: {}  
Footnote 5: email: {}  
Footnote 6: email: {}  
Footnote 7: email: {}  
Footnote 8: email: {}  
Footnote 9  
LDPC codes fully unfold their capacity-approaching error-correction capabilities under message passing decoding only if precise and computationally complex belief propagation decoding is performed. The high computational complexity is mainly induced by two properties of message passing decoding: On the one hand, to reliably exchange soft information and thus ensure optimum performance, the exchanged messages have to be represented precisely. On the other hand, elaborate arithmetic operations which combine incoming beliefs (e.g., at a check node) form a major performance bottleneck. The computational burden of high-precision message passing decoding diminishes the achievable throughput and latency and requires impractically complex implementations. Instead, practical hardware implementations use finite-precision message passing algorithms where the messages are quantized and the node operations are simplified by smart approximations. However, the error-rate performance of such finite-precision decoders deteriorates significantly with decreasing precision [9]. Recently, a fundamentally different approach was proposed: the so-called _information bottleneck_ or look-up table decoder [9; 10; 11; 12; 13; 14]. This decoder leverages ideas from information theory and machine learning and differs from conventional finite-precision decoders mainly in the following two points:  
1. Instead of executing the conventional arithmetic exactly or approximated in the nodes with discrete values, the node operations are replaced by _relevant-information-maximizing_ look-up tables which map discrete input messages onto discrete output messages. The required message mappings are designed using a _relevant-information-preserving_ clustering technique, such as the _information bottleneck method_ as shown in [10; 11] or using similar algorithms [12; 14]. 2. The _relevant-information-maximizing_ look-up tables let messages that are log-likelihood ratios (LLRs) become obsolete. Instead, integer-valued pointers to look-up table entries, sometimes called _cluster indices_, are exchanged, which do not represent LLRs. In our previous works, we have already shown that four bits are sufficient to represent the exchanged messages [10; 11; 15]: our proposed 4-bit information bottleneck decoder for regular LDPC codes approaches the performance of double precision belief-propagation decoding up to 0.1 dB over \(E_{b}/N_{0}\) with a vastly reduced implementation complexity [11]. Recently published investigations of FPGA implementations of similarly designed look-up table-based decoders in [16] showed that look-up table decoders for regular codes can achieve a throughput of 588 Gbit/s and are superior to conventional decoding techniques in terms of energy efficiency and area efficiency. However, the existing work is mainly limited to regular LDPC codes. A first step towards information bottleneck decoders for irregular LDPC codes was described in [9], where the authors advocate that existing LDPC codes are often ill-suited to information-bottleneck decoding and thus proposed a joint optimization of the node-degree distribution and the look-up tables. That is, they proposed to adapt the code to the specific shortcomings of the available information bottleneck decoding method instead of fundamentally changing the decoder design.