Refined Reliability Combining for Binary Message Passing Decoding of Product Codes
Journal article, 2021

We propose a novel soft-aided iterative decoding algorithm for product codes (PCs). The proposed algorithm, named iterative bounded distance decoding with combined reliability (iBDD-CR), enhances the conventional iterative bounded distance decoding (iBDD) of PCs by exploiting some level of soft information. In particular, iBDD-CR can be seen as a modification of iBDD where the hard decisions of the row and column decoders are made based on a reliability estimate of the BDD outputs. The reliability estimates are derived by analyzing the extrinsic message passing of generalized low-density-parity check (GLDPC) ensembles, which encompass PCs. We perform a density evolution analysis of iBDD-CR for transmission over the additive white Gaussian noise channel for the GLDPC ensemble. We consider both binary transmission and bit-interleaved coded modulation with quadrature amplitude modulation. We show that iBDD-CR achieves performance gains up to 0.51 dB compared to iBDD with the same internal decoder data flow. This makes the algorithm an attractive solution for very high-throughput applications such as fiber-optic communications.

product codes


Product codes


Message passing

quantization errors


bounded distance decoding

Binary message passing


hard decision decoding

high speed communications

Iterative decoding



Alireza Sheikh

Interuniversitair Micro-Elektronica Centrum (IMEC)

Alexandre Graell I Amat

Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks

G. Liva

German Aerospace Center (DLR)

A. Alvarado

Eindhoven University of Technology

Journal of Lightwave Technology

0733-8724 (ISSN)

Vol. 39 15 4958-4973 9435057

Subject Categories


Communication Systems

Signal Processing



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4/5/2022 7