Soft Forward Error Correction Research Articles

Performance Monitoring for Live Systems with Soft FEC and Multilevel Modulation

Performance monitoring is an essential function for margin measurements in live systems. Historically, system budgets have been described by the Q-factor converted from the bit error rate (BER) under binary modulation and direct detection. The introduction of hard-decision forward error correction (FEC) did not change this. In recent years technologies have changed significantly to comprise coherent detection, multilevel modulation and soft FEC. In such advanced systems, different metrics such as (nomalized) generalized mutual information (GMI/NGMI) and asymmetric information (ASI) are regarded as being more reliable. On the other hand, Q budgets are still useful because pre-FEC BER monitoring is established in industry for live system monitoring. The pre-FEC BER is easily estimated from available information of the number of flipped bits in the FEC decoding, which does not require knowledge of the transmitted bits that are unknown in live systems. Therefore, the use of metrics like GMI/NGMI/ASI for performance monitoring has not been possible in live systems. However, in this work we propose a blind soft-performance estimation method. Based on a histogram of log-likelihood-values without the knowledge of the transmitted bits, we show how the ASI can be estimated. We examined the proposed method experimentally for 16 and 64-ary quadrature amplitude modulation (QAM) and probabilistically shaped 16, 64, and 256-QAM in recirculating loop experiments. We see a relative error of 3.6%, which corresponds to around 0.5 dB signal-to-noise ratio difference for binary modulation, in the regime where the ASI is larger than the assumed FEC threshold. For this proposed method, the digital signal processing circuitry requires only a minimal additional function of storing the L-value histograms before the soft-decision FEC decoder.

Improving soft FEC performance for higher-order modulations via optimized bit channel mappings.

Soft forward error correction with higher-order modulations is often implemented in practice via the pragmatic bit-interleaved coded modulation paradigm, where a single binary code is mapped to a nonbinary modulation. In this paper, we study the optimization of the mapping of the coded bits to the modulation bits for a polarization-multiplexed fiber-optical system without optical inline dispersion compensation. Our focus is on protograph-based low-density parity-check (LDPC) codes which allow for an efficient hardware implementation, suitable for high-speed optical communications. The optimization is applied to the AR4JA protograph family, and further extended to protograph-based spatially coupled LDPC codes assuming a windowed decoder. Full field simulations via the split-step Fourier method are used to verify the analysis. The results show performance gains of up to 0.25 dB, which translate into a possible extension of the transmission reach by roughly up to 8%, without significantly increasing the system complexity.

Reusing Common Uncoded Experimental Data in Performance Estimation of Different FEC Codes

In this letter, we present a method for performance estimation of forward error correction (FEC) codes using off-line data without data encoding. Only a few hundred thousand uncoded symbols are used to accurately evaluate post-FEC bit error rate of soft FEC codes decodable by the sum-product algorithm at very low error rates, e.g., 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-8</sup> which is only limited by computer performance and simulation time. The method is applicable to both single and concatenated codes. The demonstration is carried out in optical 128-Gb/s polarization division multiplexed experiments with differentially encoded data and 20% redundancy quasi cyclic low-density parity check code.

Coherent MAP detection of DQPSK bits

Both IS-136 and PDC digital cellular systems employ forward error correction (FEC) encoding followed by a form of DQPSK modulation. In this letter, we derive the maximum a posteriori (MAP) bit detector for DQPSK modulation in non-ISI channels for a coherent receiver with one or more antennas. The MAP detector forms a bit log-likelihood ratio, which provides the optimal information for MLSE or MAP convolutional decoding. MAP detection requires exponentiation and logarithm operations, as well as knowledge of the noise covariance. To avoid these operations, two approximate forms are developed, which do not require the noise covariance value under certain assumptions. Both approximate approaches, when used with soft FEC decoding, are within 0.5 dB of the optimal approach.