Yunus Can Gültekin

Felipe Villenas, Yunus Can Gültekin, Alex Alvarado

We consider optical communications with intensity modulation and direct detection affected by laser relative intensity noise (RIN). Starting from a continuous-time waveform model, we derive an equivalent discrete-time channel model. As a result of RIN, the resulting channel model exhibits signal-dependent noise with memory. Unlike the commonly-assumed model in the literature, the conditional variance of this noise term has a polynomial dependence on the symbol of interest. Finally, we study achievable information rates for this channel under practically-relevant system parameters. We take a mismatched decoding approach and compute the generalized mutual information (GMI) using a memoryless decoding metric. Our numerical results show that when the memory in the channel is ignored by the receiver, GMI saturates as the constellation size increases, and thus, dense constellations do not offer gains. We also show that this saturation results from nonsymmetric nonvanishing contributions of the symbols to the GMI.

Hernan Cordova, Alexios Balatsoukas-Stimming, Yunus Can Gültekin et al.

Min-Sum (MS) decoding is a popular low-complexity alternative to belief propagation (BP), retaining only the minimum incoming message magnitude during check-node (CN) processing, at the cost of systematic message magnitude overestimation. The scaled MS (SMS) decoder compensates for this effect using a fixed scaling factor. We propose the syndrome adaptive gain Min-Sum (SAGMS) decoder for quantum low-density parity-check (QLDPC) codes, which adapts the message gain online based on the fraction of unsatisfied stabilizers, requiring no per-code or per-noise level optimization. We show that the scaling factor required for SMS to match belief propagation decreases with the CN degree, so any fixed scaling optimized for one degree incurs into a growing penalty as the CN degree varies. SAGMS avoids this limitation by adapting the gain during decoding. Simulations on generalized bicycle QLDPC codes demonstrate that SAGMS matches or outperforms the frame error rate (FER) of an offline optimized SMS decoder. Moreover, SAGMS approaches BP performance and, under certain conditions outperforms it while retaining MS-level complexity.

Yuncheng Yuan, Péter Scheepers, Lydia Tasiou et al.

This paper analyzes the design and competitiveness of four neural network (NN) architectures recently proposed as decoders for forward error correction (FEC) codes. We first consider the so-called single-label neural network (SLNN) and the multi-label neural network (MLNN) decoders which have been reported to achieve near maximum likelihood (ML) performance. Here, we show analytically that SLNN and MLNN decoders can always achieve ML performance, regardless of the code dimensions -- although at the cost of computational complexity -- and no training is in fact required. We then turn our attention to two transformer-based decoders: the error correction code transformer (ECCT) and the cross-attention message passing transformer (CrossMPT). We compare their performance against traditional decoders, and show that ordered statistics decoding outperforms these transformer-based decoders. The results in this paper cast serious doubts on the application of NN-based FEC decoders in the short and medium block length regime.

Yunus Can Gültekin, Péter Scheepers, Yuncheng Yuan et al.

We investigate the design of two neural network (NN) architectures recently proposed as decoders for forward error correction: the so-called single-label NN (SLNN) and multi-label NN (MLNN) decoders. These decoders have been reported to achieve near-optimal codeword- and bit-wise performance, respectively. Results in the literature show near-optimality for a variety of short codes. In this paper, we analytically prove that certain SLNN and MLNN architectures can, in fact, always realize optimal decoding, regardless of the code. These optimal architectures and their binary weights are shown to be defined by the codebook, i.e., no training or network optimization is required. Our proposed architectures are in fact not NNs, but a different way of implementing the maximum likelihood decoding rule. Optimal performance is numerically demonstrated for Hamming $(7,4)$, Polar $(16,8)$, and BCH $(31,21)$ codes. The results show that our optimal architectures are less complex than the SLNN and MLNN architectures proposed in the literature, which in fact only achieve near-optimal performance. Extension to longer codes is still hindered by the curse of dimensionality. Therefore, even though SLNN and MLNN can perform maximum likelihood decoding, such architectures cannot be used for medium and long codes.