Post-FEC BER Benchmarking for Bit-Interleaved Coded Modulation With Probabilistic Shaping
Journal article, 2020

Accurate performance benchmarking after forward error correction (FEC) decoding is essential for system design in optical fiber communications. Generalized mutual information (GMI) has been shown to be successful at benchmarking the bit-error rate (BER) after FEC decoding (post-FEC BER) for systems with soft-decision (SD) FEC without probabilistic shaping (PS). However, GMI is not relevant to benchmark post-FEC BER for systems with SD-FEC and PS. For such systems, normalized GMI (NGMI), asymmetric information (ASI), and achievable FEC rate have been proposed instead. They are good at benchmarking post-FEC BER or to give an FEC limit in bit-interleaved coded modulation (BICM) with PS, but their relation has not been clearly explained so far. In this article, we define generalized L-values under mismatched decoding, which are connected to the GMI and ASI. We then show that NGMI, ASI, and achievable FEC rate are theoretically equal under matched decoding but not under mismatched decoding. We also examine BER before FEC decoding (pre-FEC BER) and ASI over Gaussian and nonlinear fiber-optic channels with approximately matched decoding. ASI always shows better correlation with post-FEC BER than pre-FEC BER for BICM with PS. On the other hand, post-FEC BER can differ at a given ASI when we change the bit mapping, which describes how each bit in a codeword is assigned to a bit tributary.



bitwise decoding

mutual information


probabilistic shaping

generalized mutual information

bit-interleaved coded modulation

optical fiber communication

Benchmark testing

Forward error correction

forward error correction

Interleaved codes

Bit error rate

Probabilistic logic


Tsuyoshi Yoshida

Osaka University

Alex Alvarado

Eindhoven University of Technology

Magnus Karlsson

Chalmers, Microtechnology and Nanoscience (MC2), Photonics

Erik Agrell

Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks

Journal of Lightwave Technology

0733-8724 (ISSN) 1558-2213 (eISSN)

Vol. 38 16 4292-4306 9079569

Signal shaping in optical communications—Beyond the Gaussian channel

Swedish Research Council (VR) (2017-03702), 2018-01-01 -- 2021-12-31.

Subject Categories

Computer Engineering


Other Engineering and Technologies not elsewhere specified



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