In large-scale distributed matrix-vector multiplications, e.g., for generative AI, straggling nodes can slow down or even jeopardize the whole operation. Coded distributed computing (CDC) uses erasure codes to create redundant computations and combat stragglers. This requires encoding very large matrices. Moreover, encoding must be repeated whenever system parameters (e.g., weight matrices in AI models) evolve. This paper introduces a general framework for reducing encoding complexity in CDC. We propose the notion of an encoding blueprint, a construction schedule that specifies how each coded symbol is constructed from data and previously computed coded symbols. An optimal blueprint minimizes the number of arithmetic operations required for a given code. We first design blueprints using addition-only operations. We then extend the framework to also allow subtraction, which further decreases the number of required operations. The optimization problem is cast as a mixed-integer program (MIP), and solved. Numerical results on matrix–vector multiplication show that optimized blueprints reduce encoding operations by up to 60 percent compared to standard methods, saving billions of operations in large-scale applications. Our techniques can be used for efficient decoding as well.

Data centers (DCs) are now heavily involved in large-scale artificial intelligence (AI) learning processes. Fiber optic systems are the primary communication medium for enabling DC networks due to their high speed and low energy consumption per bit. Traditionally, fiber optic systems are designed to ensure nearly error-free communication, which increases their power consumption and latency. In this work, we revisit the communication requirements in DCs for AI training by analytically examining how communication channel noise affects the learning process. Our analysis shows that channel errors introduce bounded noise in the model weights, which can be maintained within an acceptable range. Therefore, relaxing the error-free requirement has a negligible impact on AI learning performance while significantly improving power efficiency and latency. Additionally, we propose an optimized stack layer for the optical communication link with minimal modifications to the IEEE 802.3bs standard, tailored for AI training. To validate our approach, we simulate the training of the ChatGPT-2 model on a DC with 32 workers and noisy communication links, showing that the training process tolerate a bit error rate of up to$1 \mathrm{e}-4$.

In high-rate or long-haul optical fiber transmissions, correcting chromatic dispersion (CD) is critical but challenging and energy-intensive due to the large filter tap size required for CD compensation (CDC). Overlap-save (OLS) is a common frequency-domain CDC technique that uses fast Fourier transform (FFT). However, hardware constraints-such as power, memory, latency, and chip area-limit the FFT size. This limitation makes OLS too complex or even infeasible in dispersive channels where the number of taps approaches or exceeds the FFT size. We introduce the time-segmented overlap-free (TS-OLF) technique, a novel frequency-domain block filtering method to enable low-complexity CDC under FFT-size limitations. TS-OLF divides the signal into non-overlapping blocks and segments the filter accordingly to enable filtering operations with any FFT size. It aggregates the results of different filter segments directly in the frequency domain, therefore, using a minimum number of FFT operations. We show that TS-OLF achieves consistently lower complexity than OLS when the filter size is more than half the FFT size, and unlike OLS, can handle filter sizes that exceed the FFT size. TS-OLF also outperforms other filter segmenting methods, providing significant complexity improvements.

According to the Gaussian noise (GN) model, nonlinear interference noise (NLIN) in fiber depends on the signal power spectral density (PSD). Consequently, optimizing the PSD of the pulse that modulates data, as the main factor influencing the PSD of the launched signal into the fiber, can effectively minimize fiber NLIN. In this study, we first employ the calculus of variations to identify the optimal band-limited pulse PSD that minimizes fiber NLIN. Next, we add other communication requirements, such as zero inter-symbol interference (ISI) and fast decay over time, as constraints to our design problem. For this case, we develop a general pulse model and formulate the design problem as an optimization problem. By solving this optimization problem, we find the optimal pulse PSD that not only minimizes NLIN power in fiber but also meets practical requirements. We study the time-domain impact of the designed modulating pulse PSD on the launched signal properties to gain insights into the nonlinearity benefits we achieve. We further analytically demonstrate that our designed pulse has favorable properties for the Godard timing recovery method. Through extensive simulations using the split-step Fourier method on a fiber with typical parameters and considering practical transmitter/receiver limitations, we illustrate the superior system reach and achievable data rate of our optimized pulses compared to existing pulse shapes.

Non-binary polar codes (NBPCs) decoded by successive cancellation (SC) algorithm have remarkable bit-error-rate performance compared to the binary polar codes (BPCs). Due to its serial nature, SC decoding suffers from long latency. The latency issue in BPCs has been the topic of extensive research and it has been notably resolved by the introduction of fast SC-based decoders. However, the latency problem of NBPCs is mainly untouched and the vast majority of research on NBPCs is devoted to issues concerning design and efficient implementation. In this paper, we propose fast SC decoding for NBPCs constructed based on$2\times 2$kernels. In particular, we extend the special nodes of BPCs to their non-binary counterpart and define various non-binary special nodes in the SC decoding tree of NBPCs and propose their fast decoding. This way, we avoid traversing the full decoding tree and significantly reduce the decoding delay compared to symbol-by-symbol SC decoding. We also propose a simplified NBPC structure that facilitates the procedure of non-binary fast SC decoding. Using our proposed fast non-binary decoder, we observe an improvement of more than 96% in latency concerning the original SC decoding. This is while our proposed fast SC decoder for NBPCs incurs no error-rate loss.

We introduce a novel soft-decision decoding algorithm for binary block codes named ordered reliability direct error pattern testing (ORDEPT). The proposed technique tests a list of partial error patterns (PEP)s that are arranged according to their logistic weight and completed on-the-fly based on the instantaneous received sequence and the code’s parity-check matrix. Our results, obtained for a variety of popular short high-rate codes, demonstrate that ORDEPT outperforms state-of-the-art decoding algorithms such as ordered reliability bits guessing random additive noise decoding (ORBGRAND) in terms of decoding complexity, and is hardware-favorable in terms of latency and energy consumption. The improvements carry on to the iterative decoding of product codes and convolutional product-like codes, where ORDEPT demonstrates the ability to efficiently find multiple candidate codewords and outperform state-of-the art competitors.

In this work we introduce a novel soft-decision decoding algorithm for high-rate short error-correction codes. Our results demonstrate that the proposed algorithm improves over the state-of-the-art algorithms, including recently proposed Ordered Reliability Bits Guessing Random Additive Noise Decoding (ORBGRAND), in terms of latency and decoding complexity. Specifically, we demonstrate that the ability of the proposed algorithm to find multiple candidate codewords with a reduced number of low-complexity queries makes it an efficient component decoder for iterative decoding of product-like codes.

Digital backpropagation (DBP) is the most effective fiber optic compensation technique. While DBP can increase the achievable data rate, its high computational complexity prevents its use in real-time applications. Parallelization is one of the most promising techniques to allow real-time DBP. Existing parallel DBP (PDBP) are based on coupled nonlinear Schrodinger equation (NLSE), which only considers cross-phase modulation and discards the rest of the inter-channel impairments. Therefore, these methods lose their performance in today's wavelength-division multiplexing systems. We fill this gap by proposing a PDBP capable of working with regular NLSE and compensating for all fiber impairments, including four-wave mixing. We analytically derive the compensation equations for the parallel scheme and handle them efficiently to reduce the complexity. Our simulations show a significant improvement in the sense of optimal launched power, achievable data rate, and system reach over existing DBPs with comparable complexity.

We propose a hybrid probabilistic-geometric constellation shaping method for optical fiber communication systems that is non-linearity tolerant and compatible with probabilistic fold shaping (PFS) architecture. To do so, the impact of non-linear interference noise (NLIN) in the shaping process is considered. This is a challenging process because NLIN is itself constellation dependent. This study copes with this issue by developing a deep learning-based shaping method that takes the enhanced Gaussian noise (EGN) model of fiber into account to model NLIN. Our hybrid shaping scheme maximizes the generalized mutual information (GMI) rate of the optical system while the impacts of shaping on the NLIN power are considered. Our results show that the proposed hybrid scheme results in significant reach improvements and outperforms recent hybrid shaping methods. Interestingly, our hybrid shaping scheme suggests distributions that are much different from the traditional Maxwell-Boltzmann distributions.

In this paper, the optimum tradeoff between diversity and multiplexing gains in a two-user quasi-static Rayleigh fading interference channel (IC) is studied. The diversity and multiplexing gains are two basic performance measures in wireless networks which characterize the transmission reliability and the data rate, respectively. It would be of interest to investigate the optimal tradeoff between these two measures. First, we develop a coding scheme for the two-user quasi-static Rayleigh fading Gaussian IC with interference level α := log INR/log SNR ≥ 1. Then, for this coding scheme the achievable diversity-multiplexing tradeoff (DMT) is characterized. Our achievable DMT coincides with its outer bound. In the low and high rate regions (to be defined later), the proposed coding scheme is a one-level Gaussian code, independent of the channel state information (CSI). In the middle rate region (to be defined later), the proposed coding scheme, depending on the partial CSI, can be a one-level or a two-level Gaussian code. We show that the relevant partial CSI can be represented by only one bit determined by the absolute value of the channel gain. In the middle rate region, we assume that the single-bit partial CSI for all the four channel gains of the Gaussian IC are available at both transmitters.

In this paper, the tradeoff between diversity and multiplexing gains in the two-user quasi-static Raleigh fading interference channel (IC) is derived. Under the short-term average power constraint and for the delay limited communication, we show that only a partial channel state information at the transmitter (CSIT) is enough to achieve the optimum diversity-multiplexing tradeoff (DMT) at the IC. We develop a coding scheme for the two-user quasi-static Raleigh fading IC. At the low rate region, this results in a one-level Gaussian code independent of the channel condition. At the high rate region, the result can be one-level or two-level Gaussian codes depending on the partial CSIT. The partial state information for each channel gain can be represented by only one bit corresponding to its absolute value. At the high rate region, we assume that the partial state information of all channel gains is available at the two transmit sides. The optimality of the proposed scheme is established by deriving an outer bound, which coincides with the achieved DMT.

In this paper, we consider multiple-input single-output (MISO) and single-input multiple-output (SIMO) systems, and study the diversity-multiplexing tradeoff (DMT) for them at finite signal to noise ratio (SNR). To characterize the tradeoff, the outage probability versus SNR is extracted. The diversity gain is defined as the slope at a particular SNR of the outage probability versus SNR curve and the multiplexing gain is measured as the ratio of the system spectral efficiency to the capacity of an additive white Gaussian noise (AWGN) channel. This paper provides a useful tool to examine the DMT of MISO/SIMO systems in practical (finite SNR) situation.

Considering the space division multiple access (SDMA) in IEEE 802.11a based systems, in this paper, we propose a new two-step multiuser detection (MUD) algorithms. In the first step, MMSE and MSNIR MUD algorithms are used. In the second step, by using sensitive bits algorithm (SBA) to obtain least reliable bits, maximum likelihood detection (MLD) algorithm is applied only to these bits; as a consequence, the search space is reduced dramatically. In order to reduce the computational complexity of MLD algorithm, an innovative modification named the less complex norm approximation (LCNA) based Euclidean distance is used. The performance and complexity of proposed MUD algorithms are compared with nonlinear MMSE-SIC, MSNIR-SIC and ML MUD algorithms. Results show that with a minimal penalty in performance compared to MLD algorithm, the SBA-based proposed two-step schemes have significant reduction in complexity. Furthermore, it is shown that for a specified number of sensitive bits, the introduced algorithms have approximately the same performance with significant less complexity compared to MMSE-SIC and MSNIR-SIC nonlinear MUD algorithms