Ahmed Elkelesh

Bio: Ahmed Elkelesh is an academic researcher from University of Stuttgart. The author has contributed to research in topics: Decoding methods & Belief propagation. The author has an hindex of 12, co-authored 30 publications receiving 393 citations.

Belief Propagation List Decoding of Polar Codes

Abstract: We propose a belief propagation list (BPL) decoder with comparable performance to the successive cancellation list (SCL) decoder of polar codes, which already achieves the maximum likelihood (ML) bound of polar codes for sufficiently large list size $L$ . The proposed decoder is composed of multiple parallel independent belief propagation (BP) decoders based on differently permuted polar code factor graphs. A list of possible transmitted codewords is generated and the one closest to the received vector, in terms of Euclidean distance, is picked. To the best of our knowledge, the proposed BPL decoder provides the best performance of plain polar codes under iterative decoding known so far. The proposed algorithm does not require any changes in the polar code structure itself, rendering the BPL into an alternative to the SCL decoder, equipped with a soft output capability enabling, e.g., iterative detection and decoding to further improve performance. Further benefits are the lower decoding latency than the SCL decoder and the possibility of high throughput implementations. Additionally, we show that a different selection strategy of frozen bit positions can further enhance the error-rate performance of the proposed decoder.

Belief propagation decoding of polar codes on permuted factor graphs

Abstract: We show that the performance of iterative belief propagation (BP) decoding of polar codes can be enhanced by decoding over different carefully chosen factor graph realizations. With a genie-aided stopping condition, it can achieve the successive cancellation list (SCL) decoding performance which has already been shown to achieve the maximum likelihood (ML) bound provided that the list size is sufficiently large. The proposed decoder is based on different realizations of the polar code factor graph with randomly permuted stages during decoding. Additionally, a different way of visualizing the polar code factor graph is presented, facilitating the analysis of the underlying factor graph and the comparison of different graph permutations. In our proposed decoder, a high rate Cyclic Redundancy Check (CRC) code is concatenated with a polar code and used as an iteration stopping criterion (i.e., genie) to even outperform the SCL decoder of the plain polar code (without the CRC-aid). Although our permuted factor graph-based decoder does not outperform the SCL-CRC decoder, it achieves, to the best of our knowledge, the best performance of all iterative polar decoders presented thus far.

Decoder-Tailored Polar Code Design Using the Genetic Algorithm

Abstract: We present a new framework for constructing polar codes (i.e., selecting the frozen bit positions) for arbitrary channels, tailored to a given decoding algorithm rather than assuming the (not necessarily optimal) successive cancellation (SC) decoding. The proposed framework is based on the genetic algorithm (GenAlg), where populations (i.e., collections) of information sets evolve via evolutionary transformations based on their individual error-rate performance. These populations converge toward an information set that fits both the decoding behavior and the defined channel. We construct polar codes, without the CRC-aid, tailored to plain successive cancellation list (SCL) decoding, achieving the same error-rate performance as the CRC-aided SCL decoding over both the AWGN channel and the Rayleigh channel, respectively. Furthermore, a proposed belief propagation (BP)-tailored construction approaches the SCL error-rate performance without any modifications in the decoding algorithm itself. The performance gains can be attributed to the significant reduction in the number of low-weight codewords. We show that, when required, the GenAlg can also be set up to find codes that reduce the decoding complexity. This way, the SCL list size or the number of BP iterations can be reduced while maintaining the same error-rate performance.

CRC-Aided Belief Propagation List Decoding of Polar Codes

Abstract: Although iterative decoding of polar codes has recently made huge progress based on the idea of permuted factor graphs, it still suffers from a non-negligible performance degradation when compared to state-of-the-art CRC-aided successive cancellation list (CA-SCL) decoding. In this work, we show that iterative decoding of polar codes based on the belief propagation list (BPL) algorithm can approach the error-rate performance of CA-SCL decoding and, thus, can be efficiently used for decoding the standardized 5G polar codes. Rather than only utilizing the cyclic redundancy check (CRC) as a stopping condition (i.e., for error-detection), we also aim to benefit from the error-correction capabilities of the outer CRC code. For this, we develop two distinct soft-decision CRC decoding algorithms: a Bahl-Cocke-Jelinek-Raviv (BCJR)-based approach and a sum product algorithm (SPA)-based approach. Further, an optimized selection of permuted factor graphs is analyzed and shown to reduce the decoding complexity significantly. Finally, we benchmark the proposed CRC-aided belief propagation list (CA-BPL) decoding to state-of-the-art 5G polar codes under CA-SCL decoding and, thereby, showcase an error-rate performance not just close to the CA-SCL but also close to the maximum likelihood (ML) bound as estimated by ordered statistic decoding (OSD).

Sparse Graphs for Belief Propagation Decoding of Polar Codes

Abstract: We describe a novel approach to interpret a polar code as a low-density parity-check (LDPC)-like code with an underlying sparse decoding graph. This sparse graph is based on the encoding factor graph of polar codes and is suitable for conventional belief propagation (BP) decoding. We discuss several pruning techniques based on the check node decoder (CND) and variable node decoder (VND) update equations, significantly reducing the size (i.e., decoding complexity) of the parity-check matrix. As a result, iterative polar decoding can then be conducted on a sparse graph, akin to the traditional well-established LDPC decoding, e.g., using a fully parallel sum-product algorithm (SPA). This facilitates the systematic analysis and design of polar codes using the well-established tools known from analyzing LDPC codes. We show that the proposed iterative polar decoder has a negligible performance loss for short-to-intermediate codelengths compared to Arikan's original BP decoder. Finally, the proposed decoder is shown to benefit from both reduced complexity and reduced memory requirements and, thus, is more suitable for hardware implementations.

White Paper on Broadband Connectivity in 6G

Abstract: This white paper explores the road to implementing broadband connectivity in future 6G wireless systems. Different categories of use cases are considered, from extreme capacity with peak data rates up to 1 Tbps, to raising the typical data rates by orders-of-magnitude, to support broadband connectivity at railway speeds up to 1000 km/h. To achieve these goals, not only the terrestrial networks will be evolved but they will also be integrated with satellite networks, all facilitating autonomous systems and various interconnected structures. We believe that several categories of enablers at the infrastructure, spectrum, and protocol/ algorithmic levels are required to realize the intended broadband connectivity goals in 6G. At the infrastructure level, we consider ultra-massive MIMO technology (possibly implemented using holographic radio), intelligent reflecting surfaces, user-centric and scalable cell-free networking, integrated access and backhaul, and integrated space and terrestrial networks. At the spectrum level, the network must seamlessly utilize sub-6 GHz bands for coverage and spatial multiplexing of many devices, while higher bands will be used for pushing the peak rates of point-to-point links. The latter path will lead to THz communications complemented by visible light communications in specific scenarios. At the protocol/algorithmic level, the enablers include improved coding, modulation, and waveforms to achieve lower latencies, higher reliability, and reduced complexity. Different options will be needed to optimally support different use cases. The resource efficiency can be further improved by using various combinations of full-duplex radios, interference management based on rate-splitting, machine-learning-based optimization, coded caching, and broadcasting.

Design of Polar Codes in 5G New Radio

Abstract: Polar codes have attracted the attention of academia and industry alike in the past decade, such that the $5^{\mathrm {th}}$ generation wireless systems (5G) standardization process of the $3^{\mathrm {rd}}$ generation partnership project (3GPP) chose polar codes as a channel coding scheme. In this tutorial, we provide a description of the encoding process of polar codes adopted by the 5G standard. We illustrate the struggles of designing a family of polar codes able to satisfy the demands of 5G systems, with particular attention to rate flexibility and low decoding latency. The result of these efforts is an elaborate framework that applies novel coding techniques to provide a solid channel code for NR requirements.

Belief Propagation List Decoding of Polar Codes

Abstract: We propose a belief propagation list (BPL) decoder with comparable performance to the successive cancellation list (SCL) decoder of polar codes, which already achieves the maximum likelihood (ML) bound of polar codes for sufficiently large list size $L$ . The proposed decoder is composed of multiple parallel independent belief propagation (BP) decoders based on differently permuted polar code factor graphs. A list of possible transmitted codewords is generated and the one closest to the received vector, in terms of Euclidean distance, is picked. To the best of our knowledge, the proposed BPL decoder provides the best performance of plain polar codes under iterative decoding known so far. The proposed algorithm does not require any changes in the polar code structure itself, rendering the BPL into an alternative to the SCL decoder, equipped with a soft output capability enabling, e.g., iterative detection and decoding to further improve performance. Further benefits are the lower decoding latency than the SCL decoder and the possibility of high throughput implementations. Additionally, we show that a different selection strategy of frozen bit positions can further enhance the error-rate performance of the proposed decoder.