Binary Message Passing Decoding of Product-like Codes

We propose a novel binary message passing decoding algorithm for product-like codes based on bounded distance decoding (BDD) of the component codes. The algorithm, dubbed iterative BDD with scaled reliability (iBDD-SR), exploits the channel reliabilities and is therefore soft in nature. However, the messages exchanged by the component decoders are binary (hard) messages, which significantly reduces the decoder data flow. The exchanged binary messages are obtained by combining the channel reliability with the BDD decoder output reliabilities, properly conveyed by a scaling factor applied to the BDD decisions. We perform a density evolution analysis for generalized low-density parity-check (GLDPC) code ensembles and spatially coupled GLDPC code ensembles, from which the scaling factors of the iBDD-SR for product and staircase codes, respectively, can be obtained. For the white additive Gaussian noise channel, we show performance gains up to $0.29$ dB and $0.31$ dB for product and staircase codes compared to conventional iterative BDD (iBDD) with the same decoder data flow. Furthermore, we show that iBDD-SR approaches the performance of ideal iBDD that prevents miscorrections.Comment: Accepted for publication in the IEEE Transactions on Communication

Binary Message Passing Decoding of Product-like Codes

We propose a novel binary message passing decoding algorithm for product-like codes based on bounded distance decoding (BDD) of the component codes. The algorithm, dubbed iterative BDD with scaled reliability (iBDD-SR), exploits the channel reliabilities and is therefore soft in nature. However, the messages exchanged by the component decoders are binary (hard) messages, which significantly reduces the decoder data flow. The exchanged binary messages are obtained by combining the channel reliability with the BDD decoder output reliabilities, properly conveyed by a scaling factor applied to the BDD decisions. We perform a density evolution analysis for generalized low-density parity-check (GLDPC) code ensembles and spatially coupled GLDPC code ensembles, from which the scaling factors of the iBDD-SR for product and staircase codes, respectively, can be obtained. For the white additive Gaussian noise channel, we show performance gains up to 0.29 dB and 0.31 dB for product and staircase codes compared to conventional iterative BDD (iBDD) with the same decoder data flow. Furthermore, we show that iBDD-SR approaches the performance of ideal iBDD that prevents miscorrections

Binary Message Passing Decoding of Product Codes Based on Generalized Minimum Distance Decoding

We propose a binary message passing decoding algorithm for product codes based on generalized minimum distance decoding (GMDD) of the component codes, where the last stage of the GMDD makes a decision based on the Hamming distance metric. The proposed algorithm closes half of the gap between conventional iterative bounded distance decoding (iBDD) and turbo product decoding based on the Chase--Pyndiah algorithm, at the expense of some increase in complexity. Furthermore, the proposed algorithm entails only a limited increase in data flow compared to iBDD.Comment: Invited paper to the 53rd Annual Conference on Information Sciences and Systems (CISS), Baltimore, MD, March 2019. arXiv admin note: text overlap with arXiv:1806.1090

30% Reach Increase via Low-complexity Hybrid HD/SD FEC and Nonlinearity-tolerant 4D Modulation

Current optical coherent transponders technology is driving data rates towards 1 Tb/s/{\lambda}and beyond. This trend requires both high-performance coded modulation schemes and efficient implementation of the forward-error-correction (FEC) decoder. A possible solution to this problem is combining advanced multidimensional modulation formats with low-complexity hybrid HD/SD FEC decoders. Following this rationale, in this paper we combine two recently introduced coded modulation techniques:the geometrically-shaped 4D-64 polarization ring-switched and the soft-aided bit-marking-scaled reliability decoder. This joint scheme enabled us to experimentally demonstrate the transmission of 11x218 Gbit/s channels over transatlantic distances at 5.2bit/4D-sym. Furthermore, a 30% reach increase is demonstrated over PM-8QAM and conventional HD-FEC decoding for product codes.Comment: This work has been submitted to IEEE Photonics Technology Letter

Binary Message Passing Decoding of Product Codes Based on Generalized Minimum Distance Decoding: (Invited Paper)

We propose a binary message passing decoding algorithm for product codes based on generalized minimum distance decoding (GMDD) of the component codes, where the last stage of the GMDD makes a decision based on the Hamming distance metric. The proposed algorithm closes half of the gap between conventional iterative bounded distance decoding (iBDD) and turbo product decoding based on the Chase–Pyndiah algorithm at a bit error rate of $10^{-7}$, at the expense of some increase in complexity. The proposed algorithm entails only a limited increase in data flow compared to iBDD

On Product Codes with Probabilistic Amplitude Shaping for High-Throughput Fiber-Optic Systems

Probabilistic amplitude shaping (PAS) can flexibly vary the spectral efficiency (SE) of fiber-optic systems. In this paper, we demonstrate the application of PAS to bit-wise hard decision decoding (HDD) of product codes (PCs) by finding the necessary conditions to select the PC component codes. We show that PAS with PCs and HDD yields gains up to $2.7$ dB and SE improvement up to approximately $1$ bit/channel use compared to using PCs with uniform signaling and HDD. Furthermore, we employ the recently introduced iterative bounded distance decoding with combined reliability of PCs to improve performance of PAS with PCs and HDD.Comment: Accepted for publication in IEEE Communications Letter

Improved Soft-aided Decoding of Product Codes with Dynamic Reliability Scores

Products codes (PCs) are conventionally decoded with efficient iterative bounded-distance decoding (iBDD) based on hard-decision channel outputs which entails a performance loss compared to a soft-decision decoder. Recently, several hybrid algorithms have been proposed aimed to improve the performance of iBDD decoders via the aid of a certain amount of soft information while keeping the decoding complexity similarly low as in iBDD. We propose a novel hybrid low-complexity decoder for PCs based on error-and-erasure (EaE) decoding and dynamic reliability scores (DRSs). This decoder is based on a novel EaE component code decoder, which is able to decode beyond the designed distance of the component code but suffers from an increased miscorrection probability. The DRSs, reflecting the reliability of a codeword bit, are used to detect and avoid miscorrections. Simulation results show that this policy can reduce the miscorrection rate significantly and improves the decoding performance. The decoder requires only ternary message passing and a slight increase of computational complexity compared to iBDD, which makes it suitable for high-speed communication systems. Coding gains of up to 1.2 dB compared to the conventional iBDD decoder are observed.Comment: Submitted to IEE

One and Two Bit Message Passing for SC-LDPC Codes with Higher-Order Modulation

Low complexity decoding algorithms are necessary to meet data rate requirements in excess of 1 Tbps. In this paper, we study one and two bit message passing algorithms for belief propagation decoding of low-density parity-check (LDPC) codes and analyze them by density evolution. The variable nodes (VNs) exploit soft information from the channel output. To decrease the data flow, the messages exchanged between check nodes (CNs) and VNs are represented by one or two bits. The newly proposed quaternary message passing (QMP) algorithm 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 for high throughput forward error correction, spatially coupled LDPC codes and a target spectral efficiency (SE) of 3 bits/QAM symbol are considered. Gains of about 0.7 dB and 0.1 dB are observed compared to BMP and TMP, respectively. The gap to unquantized belief propagation (BP) decoding is reduced to about 0.75 dB. For smaller code rates, the gain of QMP compared to TMP is more pronounced and amounts to 0.24 dB in the considered example.Comment: Accepted for IEEE/OSA Journal on Lightwave Technolog