Successive Interference Cancellation for Bandlimited Channels with Direct Detection

Oversampling increases information rates for bandlimited channels with direct detection, but joint detection and decoding (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) with multi-level coding. 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 classic 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 and higher-order modulation confirm the predicted rate and energy gains.Comment: Submitted to IEEE Journal of Lightwave Technology on December 15, 2022; Resubmitted to IEEE Transactions on Communications on September 9, 2023

Polar Coded Faster-than-Nyquist (FTN) Signaling with Symbol-by-Symbol Detection

Reduced complexity faster-than-Nyquist (FTN) signaling systems are gaining increased attention as they provide improved bandwidth utilization for an acceptable level of detection complexity. In order to have a better understanding of the tradeoff between performance and complexity of the reduced complexity FTN detection techniques, it is necessary to study these techniques in the presence of channel coding. In this paper, we investigate the performance a polar coded FTN system which uses a reduced complexity FTN detection, namely, the recently proposed successive symbol-by-symbol with go-backK sequence estimation (SSSgbKSE) technique. Simulations are performed for various intersymbol-interference (ISI) levels and for various go-back-K values. Bit error rate (BER) performance of Bahl-Cocke-Jelinek-Raviv (BCJR) detection and SSSgbKSE detection techniques are studied for both uncoded and polar coded systems. Simulation results reveal that polar codes can compensate some of the performance loss incurred in the reduced complexity SSSgbKSE technique and assist in closing the performance gap between BCJR and SSSgbKSE detection algorithms

Fast Polarization for Processes with Memory

Fast polarization is crucial for the performance guarantees of polar codes. In the memoryless setting, the rate of polarization is known to be exponential in the square root of the block length. A complete characterization of the rate of polarization for models with memory has been missing. Namely, previous works have not addressed fast polarization of the high entropy set under memory. We consider polar codes for processes with memory that are characterized by an underlying ergodic finite-state Markov chain. We show that the rate of polarization for these processes is the same as in the memoryless setting, both for the high and for the low entropy sets.Comment: 17 pages, 3 figures. Submitted to IEEE Transactions on Information Theor

Data-Driven Neural Polar Codes for Unknown Channels With and Without Memory

In this work, a novel data-driven methodology for designing polar codes for channels with and without memory is proposed. The methodology is suitable for the case where the channel is given as a "black-box" and the designer has access to the channel for generating observations of its inputs and outputs, but does not have access to the explicit channel model. The proposed method leverages the structure of the successive cancellation (SC) decoder to devise a neural SC (NSC) decoder. The NSC decoder uses neural networks (NNs) to replace the core elements of the original SC decoder, the check-node, the bit-node and the soft decision. Along with the NSC, we devise additional NN that embeds the channel outputs into the input space of the SC decoder. The proposed method is supported by theoretical guarantees that include the consistency of the NSC. Also, the NSC has computational complexity that does not grow with the channel memory size. This sets its main advantage over successive cancellation trellis (SCT) decoder for finite state channels (FSCs) that has complexity of $O(|\mathcal{S}|^3 N\log N)$, where $|\mathcal{S}|$ denotes the number of channel states. We demonstrate the performance of the proposed algorithms on memoryless channels and on channels with memory. The empirical results are compared with the optimal polar decoder, given by the SC and SCT decoders. We further show that our algorithms are applicable for the case where there SC and SCT decoders are not applicable

Algorithmic Polarization for Hidden Markov Models

Using a mild variant of polar codes we design linear compression schemes compressing Hidden Markov sources (where the source is a Markov chain, but whose state is not necessarily observable from its output), and to decode from Hidden Markov channels (where the channel has a state and the error introduced depends on the state). We give the first polynomial time algorithms that manage to compress and decompress (or encode and decode) at input lengths that are polynomial both in the gap to capacity and the mixing time of the Markov chain. Prior work achieved capacity only asymptotically in the limit of large lengths, and polynomial bounds were not available with respect to either the gap to capacity or mixing time. Our results operate in the setting where the source (or the channel) is known. If the source is unknown then compression at such short lengths would lead to effective algorithms for learning parity with noise - thus our results are the first to suggest a separation between the complexity of the problem when the source is known versus when it is unknown

Achievable Information Rates and Concatenated Codes for the DNA Nanopore Sequencing Channel

The errors occurring in DNA-based storage are correlated in nature, which is a direct consequence of the synthesis and sequencing processes. In this paper, we consider the memory-$k$ nanopore channel model recently introduced by Hamoum et al., which models the inherent memory of the channel. We derive the maximum a posteriori (MAP) decoder for this channel model. The derived MAP decoder allows us to compute achievable information rates for the true DNA storage channel assuming a mismatched decoder matched to the memory-$k$ nanopore channel model, and quantify the loss in performance assuming a small memory length--and hence limited decoding complexity. Furthermore, the derived MAP decoder can be used to design error-correcting codes tailored to the DNA storage channel. We show that a concatenated coding scheme with an outer low-density parity-check code and an inner convolutional code yields excellent performance.Comment: This paper has been accepted and awaiting publication in informatio theory workshop (ITW) 202