Spatially coupled serially concatenated codes (SC-SCCs) are constructed by coupling several classical turbo-like component codes. The resulting spatially coupled codes provide a close-to-capacity performance and low error floor, which have attracted a lot of interest in the past few years. The aim of this paper is to perform a comprehensive design space exploration to reveal different aspects of SC-SCCs, which is missing in the literature. More specifically, we investigate the effect of block length, coupling memory, decoding window size, and number of iterations on the decoding performance, complexity, latency, and throughput of SC-SCCs. To this end, we propose two decoding algorithms for the SC-SCCs: block-wise and window-wise decoders. For these, we present VLSI architectural templates and explore them based on building blocks implemented in 12nm FinFET technology. Linking architectural templates with the new algorithms, we demonstrate various tradeoffs between throughput, silicon area, latency, and decoding performance.

In Message Passing (MP) decoding of Low-Density Parity Check (LDPC) codes, extrinsic information is exchanged between Check Nodes (CNs) and Variable Nodes (VNs). In a practical implementation, this information exchange is limited by quantization using only a small number of bits. In recent investigations, a novel class of Finite Alphabet Message Passing (FA-MP) decoders are designed to maximize the Mutual Information (MI) using only a small number of bits per message (e.g., 3 or 4 bits) with a communication performance close to high-precision Belief Propagation (BP) decoding. In contrast to the conventional BP decoder, operations are given as discrete-input discrete-output mappings which can be described by multidimensional LUTs (mLUTs). A common approach to avoid exponential increases in the size of mLUTs with the node degree is given by the sequential LUT (sLUT) design approach, i.e., by using a sequence of two-dimensional Lookup-Tables (LUTs) for the design, leading to a slight performance degradation. Recently, approaches such as Reconstruction-Computation-Quantization (RCQ) and Mutual Information-Maximizing Quantized Belief Propagation (MIM-QBP) have been proposed to avoid the complexity drawback of using mLUTs by using pre-designed functions that require calculations over a computational domain. It has been shown that these calculations are able to represent the mLUT mapping exactly by executing computations with infinite precision over real numbers. Based on the framework of MIM-QBP and RCQ, the Minimum-Integer Computation (MIC) decoder design generates low-bit integer computations that are derived from the Log-Likelihood Ratio (LLR) separation property of the information maximizing quantizer to replace the mLUT mappings either exactly or approximately. We derive a novel criterion for the bit resolution that is required to represent the mLUT mappings exactly. Furthermore, we show that our MIC decoder has exactly the communication performance of the corresponding mLUT decoder, but with much lower implementation complexity. We also perform an objective comparison between the state-of-the-art Min-Sum (MS) and the FA-MP decoder implementations for throughput towards 1 Tb/s in a state-of-the-art 28 nm Fully-Depleted Silicon-on-Insulator (FD-SOI) technology. Furthermore, we demonstrate that our new MIC decoder implementation outperforms previous FA-MP decoders and MS decoders in terms of reduced routing complexity, area efficiency and energy efficiency.

In the field of communication, autoencoder (AE) refers to a system that replaces parts of the traditional transmitter and receiver with artificial neural networks (ANNs). To meet the system performance requirements, it is necessary for the AE to adapt to the changing wireless-channel conditions at runtime. Thus, online fine-tuning in the form of ANN-retraining is of great importance. Many algorithms on the ANN layer are developed to improve the AE’s performance at the communication layer. Yet, the link of the system performance and the ANN topology to the hardware layer is not fully explored. In this paper, we analyze the relations between the design layers and present a hardware implementation of an AE-based demapper that enables fine-tuning to adapt to varying channel conditions. As a platform, we selected field-programmable gate arrays (FPGAs) which provide high flexibility and allow to satisfy the low-power and low-latency requirements of embedded communication systems. Furthermore, our cross-layer approach leverages the flexibility of FPGAs to dynamically adapt the degree of parallelism (DOP) to satisfy the system-level requirements and to ensure environmental adaptation. Our solution achieves 2000× higher throughput than a high-performance graphics processor unit (GPU), draws 5× less power than an embedded central processing unit (CPU) and is 5800× more energy efficient compared to an embedded GPU for small batch size. To the best of our knowledge, such a cross-layer design approach combined with FPGA implementation is unprecedented.

Low-density parity-check (LDPC) codes are a well-established class of forward error correction codes that provide excellent error correction performance for large code block sizes. However, for throughputs toward 1 Tbit/s, as expected for B5G systems, state-of-the-art LDPC soft decoders are restricted to short code block sizes of several hundred to thousands of bits due to routing congestion challenges, limiting the overall communications performance of the transmission system. Spatially coupled LDPC (SC-LDPC) codes and respective sliding window decoding methods show the potential to overcome these block size restrictions. However, in contrast to conventional LDPC codes little literature exists on the efficient hardware implementation of respective high-throughput decoders. In this work, we present the first in-depth investigation on the implementation of SC-LDPC decoders for throughputs beyond 100 Gbit/s. For an $$N=51328$$N = 51328 , $$R=0.8$$R = 0.8 terminated SC-LDPC code with sub-block size $$c=640$$c = 640 and coupling width $$m_s=1$$m s = 1 , we explore various design trade-offs, including row- and column-wise decoding, non-overlapping and overlapping window scheduling, and processor pipelining. To the best of our knowledge, this is the first description of a column-wise SC-LDPC decoding architecture in the literature. We complement the algorithmic investigation with the virtual silicon implementation of all presented decoders in a 22nm FD-SOI technology.

In communication systems, autoencoder refers to a system that replaces parts of the traditional transmitter and receiver of the baseband processing chain with artificial neural networks (ANNs). This allows to jointly train the system for an underlying channel model by reconstructing the input symbols at the output. Since the actual behavior of a real communication channel cannot be perfectly reproduced by an abstract model, it is necessary for the autoencoder to adapt to the changing conditions at runtime. Thus, online fine-tuning, in the form of ANN-retraining is of great importance. A platform able to satisfy the low-latency and low-power requirements of embedded communication systems are Field-programmable gate arrays (FPGAs). In this paper, we present an online-trainable low-power FPGA architecture for the receiver of an autoencoder-based communication chain. The architecture is embedded into an exploration framework that automatically determines the optimal degree of parallelism to minimize latency or power consumption. Our solutions achieve 2000×higher throughput than a high-performance GPU, draw 5×less power than an embedded CPU and are 5800×more energy efficient compared to an embedded GPU, for a batch size of one. To the best of our knowledge, this is the first FPGA-based autoencoder implementation for communication systems.