Channel coding plays a pivotal role in ensuring reliable communication over wireless channels. With the growing need for ultra-reliable communication in emerging wireless use cases, the significance of channel coding ...
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Channel coding plays a pivotal role in ensuring reliable communication over wireless channels. With the growing need for ultra-reliable communication in emerging wireless use cases, the significance of channel coding has amplified. Furthermore, minimizing decoding latency is crucial for critical-mission applications, while optimizing energy efficiency is paramount for mobile and the Internet of Things (IoT) communications. As the fifth generation (5G) of mobile communications is currently in operation and 5G-advanced is on the horizon, the objective of this paper is to assess prominent channel coding schemes in the context of recent advancements and the anticipated requirements for the sixth generation (6G). In this paper, after considering the potential impact of channel coding on key performance indicators (KPIs) of wireless networks, we review the evolution of mobile communication standards and the organizations involved in the standardization, from the first generation (1G) to the current 5G, highlighting the technologies integral to achieving targeted KPIs such as reliability, data rate, latency, energy efficiency, spectral efficiency, connection density, and traffic capacity. Following this, we delve into the anticipated requirements for potential use cases in 6G. The subsequent sections of the paper focus on a comprehensive review of three primary coding schemes utilized in past generations and their recent advancements: low-density parity-check (LDPC) codes, turbo codes (including convolutional codes), and polar codes (alongside Reed-Muller codes). Additionally, we examine alternative coding schemes like Fountain codes (also known as rate-less codes), sparse regression codes, among others. Our evaluation includes a comparative analysis of error correction performance and the performance of hardware implementation for these coding schemes, providing insights into their potential and suitability for the upcoming 6G era. Lastly, we will briefly explore consider
sparse superposition codes, or sparse regression codes, constitute a new class of codes, which was first introduced for communication over the additive white Gaussian noise (AWGN) channel. It has been shown that such ...
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sparse superposition codes, or sparse regression codes, constitute a new class of codes, which was first introduced for communication over the additive white Gaussian noise (AWGN) channel. It has been shown that such codes are capacity-achieving over the AWGN channel under optimal maximum-likelihood decoding as well as under various efficient iterative decoding schemes equipped with power allocation or spatially coupled constructions. Here, we generalize the analysis of these codes to a much broader setting that includes all memoryless channels. We show, for a large class of memoryless channels, that spatial coupling allows an efficient decoder, based on the generalized approximate message-passing (GAMP) algorithm, to reach the potential (or Bayes optimal) threshold of the underlying (or uncoupled) code ensemble. Moreover, we argue that spatially coupled sparse superposition codes universally achieve capacity under GAMP decoding by showing, through analytical computations, that the error floor vanishes and the potential threshold tends to capacity, as one of the code parameters goes to infinity. Furthermore, we provide a closed-form formula for the algorithmic threshold of the underlying code ensemble in terms of Fisher information. Relating an algorithmic threshold to a Fisher information has theoretical as well as practical importance. Our proof relies on the state evolution analysis and uses the potential method developed in the theory of low-density parity-check (LDPC) codes and compressed sensing.
In this paper, we continue our investigation into the error-reducing properties of superposition codes started in Andreev, et al. (2023), where the focus was on sparse regression codes (SPARCs) with Gaussian signals. ...
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ISBN:
(纸本)9798350362527;9798350362510
In this paper, we continue our investigation into the error-reducing properties of superposition codes started in Andreev, et al. (2023), where the focus was on sparse regression codes (SPARCs) with Gaussian signals. However, despite their high performance, SPARCs are known to have noticeable limitations in their application due to their high decoding complexity. This prompted us to propose a Low-Density Parity Check (LDPC)-based superposition scheme with low-complexity Soft Successive Interference Cancellation (SIC) decoding. In this paper, we focus on such a scheme and perform a detailed analysis of it. We have developed a low-complexity quantized density evolution (DE) procedure for the proposed scheme under the SIC decoder to estimate the output bit error rate. It is shown that the obtained DE procedure quite accurately predicts the behavior of the considered LDPC-based superposition scheme. The procedure predicts not only the waterfall region, but also the errorfloor region, which we assume to be caused by interference of component LDPC codes. This helps us to obtain highly optimized constructions of proto-graphs of LDPC code components and significantly improve the bit error rate performance of the whole construction. In addition, for the proposed scheme we have analyzed the output error count distribution, which is crucial for concatenated code constructions, where usually error-reducing codes are used as inner code. All numerical results and analysis are presented at the end of the paper.
sparse regression codes with approximate message passing (AMP) decoding have gained much attention in recent times. The concepts underlying this coding scheme extend to unsourced access with coded compressed sensing (...
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ISBN:
(纸本)9781728164328
sparse regression codes with approximate message passing (AMP) decoding have gained much attention in recent times. The concepts underlying this coding scheme extend to unsourced access with coded compressed sensing (CCS), as first pointed out by Fengler, Jung, and Caire. More specifically, their approach uses a concatenated coding framework with an inner AMP decoder followed by an outer tree decoder. In the original implementation, these two components work independently of each other, with the tree decoder acting on the static output of the AMP decoder. This article introduces a novel framework where the inner AMP decoder and the outer tree decoder operate in tandem, dynamically passing information back and forth to take full advantage of the underlying CCS structure. The enhanced architecture exhibits significant performance benefit over a range of system parameters.
Novel sparseregression LDPC (SR-LDPC) codes exhibit excellent performance over additive white Gaussian noise (AWGN) channels in part due to their natural provision of shaping gains. Though SR-LDPC-like codes have bee...
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ISBN:
(纸本)9798350382853;9798350382846
Novel sparseregression LDPC (SR-LDPC) codes exhibit excellent performance over additive white Gaussian noise (AWGN) channels in part due to their natural provision of shaping gains. Though SR-LDPC-like codes have been considered within the context of single-user error correction and massive random access, they are yet to be examined as candidates for coordinated multi-user communication scenarios. This article explores this gap in the literature and demonstrates that SR-LDPC codes, when combined with coded demixing techniques, offer a new framework for efficient non-orthogonal multiple access (NOMA) in the context of coordinated multi-user communication channels. The ensuing communication scheme is referred to as MU-SR-LDPC coding. Empirical evidence suggests that MU-SR-LDPC coding can increase the sum-rate for a fixed Eb/N0 when compared to orthogonal multiple access (OMA) techniques such as time division multiple access (TDMA) or frequency division multiple access (FDMA). Importantly, MU-SR-LDPC coding enables a pragmatic solution path for user-centric cell-free communication systems with (local) joint decoding. Results are supported by numerical simulations.
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