Performance Evaluation

Performance evaluation of digital coherent optical systems using simulation and experiments poses new and interesting challenges. In optical systems, bit error rate (BER) values below 10 −15 are expected. Such low values are only achieved after advanced forward error correction (FEC) schemes. Until recently, optical communication systems were designed to achieve a certain pre-FEC BER (BERpre), aiming at a post-FEC BER (BERpost) below 10 −15 . However, in modern digital coherent optical systems deploying advanced coded modulation and soft-decision FEC schemes, BERpre becomes insufficient to predict BERpost. This chapter addresses conventional and information-theoretic metrics for performance evaluation considering implementation constraints of modulation and coding. We introduce the metrics of mutual information (MI) and generalized mutual information (GMI), and present analytic and computational methods for their calculation.

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Notes

HD decoders can also exploit reliability information [2,3,4]. However, we consider here standard HD decoders designed to minimize metrics based on the Hamming distance.

Uppercase letters (e.g., X) indicate random variables, with their realizations being indicated by lower case letters (e.g., x). The alphabets are indicated by calligraphic letters (e.g., \(\mathcal \) ). Boldface uppercase letters (e.g., X) indicate vectors of random variables. Boldface lowercase letters (e.g., x) indicate vectors of realizations of random variables.

Some HD decoders for Staircase codes use strategies based on the Hamming distance metric [4]. The Hamming distance between two sequences A and \(\hat <\mathbf >\) is the number of elements in which they differ from each other.

BICM schemes have bit interleaving. In certain codes, e.g., for low-density parity-check (LDPC) codes, interleaving can be implicit in the parity-check matrix.

Some CM schemes with binary FEC codes also have the MI as a relevant metric. These schemes are out of the scope of this book. Some examples are BICM schemes that employ iterations between the SD-BW demapper and the binary SD-FEC decoder, and MLC schemes with multi-stage decoding. For more details, we refer the reader to [21] and [22].

The rate R can be interpreted as the rate of a coded modulation scheme.

As previously discussed, the MI is also a relevant metric for some binary CM schemes, e.g., BICM schemes with iterative decoding and MLC schemes with multi-stage decoding.

Note that, if q(x, y) = f Y |X(y|x) and a = 1, (8.30) reduces to (8.13), where \(f_Y(y) = \sum _^p_X(x_j)f_(y,x_j)\) .

Under the theory of mismatched decoding, we can use the GMI expression to obtain an AIR for non-binary CM schemes with HD-SW decoders based on the Hamming distance metric.

In all simulation problems, transmit signals with at least 2 16 symbols per polarization orientation. Consider optical modulation and coherent detection in the simulation models.

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Author information

Authors and Affiliations

  1. School of Electrical & Computer Engineering, University of Campinas, Campinas, Brazil Darli Augusto de Arruda Mello & Fabio Aparecido Barbosa
  1. Darli Augusto de Arruda Mello