Performance Metrics for Systems with Soft-Decision FEC and Probabilistic Shaping

High-throughput optical communication systems utilize binary soft-decision forward error correction (SD-FEC) with bit interleaving over the bit channels. The generalized mutual information (GMI) is an achievable information rate (AIR) in such systems and is known to be a good predictor of the bit error rate after SD-FEC decoding (post-FEC BER) for uniform signaling. However, for probabilistically shaped (nonuniform) signaling, we find that the normalized AIR, defined as the AIR divided by the signal entropy, is less correlated with the post-FEC BER. We show that the information quantity based on the distribution of the single bit signal, and its asymmetric loglikelihood ratio, are better predictors of the post-FEC BER. In simulations over the Gaussian channel, we find that the prediction accuracy, quantified as the peak-to-peak deviation of the post-FEC BER within a set of different modulation formats and distributions, can be improved more than 10 times compared with the normalized AIR.Comment: 4 pages, 3 figure

Hierarchical Distribution Matching for Probabilistically Shaped Coded Modulation

The implementation difficulties of combining distribution matching (DM) and dematching (invDM) for probabilistic shaping (PS) with soft-decision forward error correction (FEC) coding can be relaxed by reverse concatenation, for which the FEC coding and decoding lies inside the shaping algorithms. PS can seemingly achieve performance close to the Shannon limit, although there are practical implementation challenges that need to be carefully addressed. We propose a hierarchical DM (HiDM) scheme, having fully parallelized input/output interfaces and a pipelined architecture that can efficiently perform the DM/invDM without the complex operations of previously proposed methods such as constant composition DM (CCDM). Furthermore, HiDM can operate at a significantly larger post-FEC bit error rate (BER) for the same post-invDM BER performance, which facilitates simulations. These benefits come at the cost of a slightly larger rate loss and required signal-to-noise ratio at a given post-FEC BER.Comment: 11 pages, 7 figure

Joint Source-Channel Coding via Compressed Distribution Matching in Fiber-Optic Communications

The variability of source entropy due to data idling is inconsistent with most studies\u27 assumptions in probabilistic shaping. We propose a distribution matcher sensitive to the source entropy, and discuss its impacts on fiber-optic communications

Performance Prediction Recipes for Optical Links

Although forward error-correction (FEC) coding is an essential part of modern fiber-optic communication systems, it is impractical to implement and evaluate FEC in transmission experiments and simulations. Therefore, it is desirable to accurately predict the end-to-end link performance including FEC from transmission data recorded without FEC. In this tutorial, we provide ready-to-implement "recipes" for such prediction techniques, which apply to arbitrary channels and require no knowledge of information or coding theory. The appropriate choice of recipe depends on properties of the FEC encoder and decoder. The covered metrics include bit error rate, symbol error rate, achievable information rate, and asymptotic information, in all cases computed using a mismatched receiver. Supplementary software implementations are available

The 5′-AT-rich half-site of Maf recognition element: a functional target for bZIP transcription factor Maf

The Maf family of proteins are a subgroup of basic region-leucine zipper (bZIP) transcription factors, which recognize a long palindromic DNA sequence [TGCTGAC(G)TCAGCA] known as the Maf recognition element (MARE). Interestingly, the functional target enhancer sequences present in the αA-crystallin gene contain a well-conserved half-site of MARE rather than the entire palindromic sequence. To resolve how Maf proteins bind to target sequences containing only MARE half-sites, we examined their binding activities using electrophoretic gel mobility shift assays as well as in vitro and in vivo reporter assays. Our results indicate that the 5′-flanking region of the MARE half-site is required for Maf proteins to bind both in vitro and in vivo. The critical 5′-flanking sequences for c-Maf were determined by a selection and amplification binding assay and show a preference for AT-rich nucleotides. Furthermore, sequence analysis of the regulatory regions of several target genes also suggests that AT-rich sequences are important. We conclude that Maf can bind to at least two types of target sequences, the classical MARE (palindrome type) and a 5′-AT-rich MARE half-site (half-site type). Our results provide important new insights into the DNA binding and site selection by bZIP transcription factors