Reliable communication over bandlimited and nonlinear channels usually requires equalization to simplify receiver processing. Equalizers that perform joint detection and decoding (JDD) achieve the highest information rates but are often too complex to implement. To address this challenge, model-based neural network (NN) equalizers that perform successive interference cancellation (SIC) are shown to approach JDD information rates for bandlimited channels with a memoryless nonlinearity and additive white Gaussian noise. The NNs are chosen to have a periodically time-varying and recurrent structure that imitates the forward-backward algorithm (FBA) in every SIC stage. Simulations for short-haul fiber-optic links with square-law detection show that NN-SIC nearly doubles current spectral efficiencies, and bipolar or complex-valued modulations achieve energy gains of up to 3 dB compared to state-of-the-art intensity modulation. Moreover, NN-SIC is considerably less complex than equalizers that perform JDD, mismatched FBA processing, and Gibbs sampling.

Neural networks (NNs) inspired by the forward-backward algorithm (FBA) are used as equalizers for bandlimited channels with a memoryless nonlinearity. The NN-equalizers are combined with successive interference cancellation (SIC) to approach the information rates of joint detection and decoding (JDD) with considerably less complexity than JDD and other existing equalizers. Simulations for short-haul optical fiber links with square-law detection illustrate the gains.

The maximum information rates for bandlimited channels with direct detection are achieved with joint detection and decoding (JDD), but JDD is often too complex to implement. Two receiver structures are studied to reduce complexity: separate detection and decoding (SDD) and successive interference cancellation (SIC). For bipolar modulation, frequency-domain raised-cosine pulse shaping, and fiber-optic channels with chromatic dispersion, SIC achieves rates close to those of JDD, thereby attaining significant energy gains over SDD and intensity modulation. Gibbs sampling further reduces the detector complexity and achieves rates close to those of the forward-backward algorithm at low to intermediate signal-to-noise ratio (SNR) but stalls at high SNR. Simulations with polar codes, higher-order modulation, and multi-level coding confirm the predicted gains.

This paper applies probabilistic amplitude shaping (PAS) to cyclic redundancy check (CRC)-aided tail-biting trellis-coded modulation (TCM). CRC-TCM-PAS produces practical codes for short block lengths on the additive white Gaussian noise (AWGN) channel. In the transmitter, equally likely message bits are encoded by a distribution matcher (DM) generating amplitude symbols with a desired distribution. A CRC is appended to the sequence of amplitude symbols, and this sequence is then encoded and modulated by TCM to produce real-valued channel input signals. This paper proves that the sign values produced by the TCM are asymptotically equally likely to be positive or negative. The CRC-TCM-PAS scheme can thus generate channel input symbols with a symmetric capacity-approaching probability mass function. The paper provides an analytical upper bound on the frame error rate of the CRC-TCM-PAS system over the AWGN channel. This FER upper bound is the objective function used for jointly optimizing the CRC and convolutional code. Additionally, this paper proposes a multi-composition DM, which is a collection of multiple constant-composition DMs. The optimized CRC-TCM-PAS systems achieve frame error rates below the random coding union (RCU) bound in AWGN and outperform the short-blocklength PAS systems with various other forward error correction codes studied in Coşkun et al. (2019).

A multilevel coded modulation scheme is studied that uses solely binary polar codes and Honda-Yamamoto probabilistic shaping. The scheme is shown to achieve the capacity of discrete memoryless channels with input alphabets of cardinality a power of two. The performance of finite-length implementations is compared to polar-coded probabilistic amplitude shaping and constant composition distribution matching.

Several applications in communication, control, and learning require approximating target distributions to within small informational divergence. The additional requirement of invertibility usually leads to using encoders that are one-to-one mappings, also known as distribution matchers. However, even the best one-to-one encoders have divergences that grow logarithmically with the block length. To overcome this limitation, an encoder is proposed that has an invertible one-to-many mapping and a low-rate random number generator (RNG). Two algorithms are developed to design the mapping by assigning strings in either a most-likely first or least-likely first order. Both algorithms give information rates approaching the entropy of the target distribution with exponentially decreasing divergence and with vanishing RNG rate in the block length.

Polar codes are designed for parallel binary-input additive white Gaussian noise (BiAWGN) channels with an average power constraint. The two main design choices are: the mapping between codeword bits and channels of different quality, and the power allocation under the average power constraint. Information theory suggests to allocate power such that the sum of mutual information (MI) terms is maximized. However, a power allocation specific to polar codes shows significant gains.