arXiv subjects

Ahmed Elkelesh

Publications and source records attributed to Ahmed Elkelesh.

At least 19 recordsLinked to original sources

arXiv2026

Enhanced Feedback Mechanisms for Resource-Efficient Incremental Redundancy

Incremental redundancy (IR) can reduce error rates by spreading coded bits across multiple transmission attempts. However, conventional stop-and-wait operation with coarse feedback often over-provisions retransmissions, triggers unnecessary decoding attempts, and increases end-to-end latency. This paper develops enhanced feedback and scheduling mechanisms that predict the additional redundancy needed for successful decoding and allocate only the required resources. We study two complementary strategies. First, using channel statistics, we learn a one- or two-shot mapping from channel quality to the minimum redundancy budget. As a byproduct, we derive an achievable reliability lower bound on the error probability of hybrid automatic repeat request (HARQ) systems. Numerical results with polar-coded IR-HARQ scheme show that the bound can be closely approached by appropriately selecting the second-transmission redundancy over a wide SNR range with savings up to 60\% in retransmission size. Second, we propose a realization-aware early-feedback mechanism that uses first-transmission reliability information to make per-codeword decisions before decoding: whether the codeword is already decodable, if not, how many additional redundancy versions are needed, or whether decoding is unlikely and rate adaptation is preferable. Link-level simulations with 5G NR LDPC codes show that both predictors achieve high accuracy (about 96\% in our study), increasing the probability of successful decoding within at most two transmission occasions.

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arXiv2026

Hybrid Resource Allocation Scheme for Bistatic ISAC with Data Channels

Bistatic integrated sensing and communication (ISAC) enables efficient reuse of the existing cellular infrastructure and is likely to play an important role in future sensing networks. In this context, ISAC using the data channel is a promising approach to improve the bistatic sensing performance compared to relying solely on pilots. One of the challenges associated with this approach is resource allocation: the communication link aims to transmit higher modulation order (MO) symbols to maximize the throughput, whereas a lower MO is preferable for sensing to achieve a higher signal-to-noise ratio in the radar image. To address this conflict, this paper introduces a hybrid resource allocation scheme. By placing lower MO symbols as pseudo-pilots on a suitable sensing grid, we enhance the bistatic sensing performance while only slightly reducing the spectral efficiency of the communication link. Simulation results validate our approach against different baselines and provide practical insights into how decoding errors affect the sensing performance.

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arXiv2022

Graph Search based Polar Code Design

It is well known that to fulfill their full potential, the design of polar codes must be tailored to their intended decoding algorithm. While for successive cancellation (SC) decoding, information theoretically optimal constructions are available, the code design for other decoding algorithms (such as belief propagation (BP) decoding) can only be optimized using extensive Monte Carlo simulations. We propose to view the design process of polar codes as a graph search problem and thereby approaching it more systematically. Based on this formalism, the design-time complexity can be significantly reduced compared to state-of-the-art Genetic Algorithm (GenAlg) and deep learning-based design algorithms. Moreover, sequences of rate-compatible polar codes can be efficiently found. Finally, we analyze both the complexity of the proposed algorithm and the error-rate performance of the constructed codes.

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arXiv2022

Learning Quantization in LDPC Decoders

Finding optimal message quantization is a key requirement for low complexity belief propagation (BP) decoding. To this end, we propose a floating-point surrogate model that imitates quantization effects as additions of uniform noise, whose amplitudes are trainable variables. We verify that the surrogate model closely matches the behavior of a fixed-point implementation and propose a hand-crafted loss function to realize a trade-off between complexity and error-rate performance. A deep learning-based method is then applied to optimize the message bitwidths. Moreover, we show that parameter sharing can both ensure implementation-friendly solutions and results in faster training convergence than independent parameters. We provide simulation results for 5G low-density parity-check (LDPC) codes and report an error-rate performance within 0.2 dB of floating-point decoding at an average message quantization bitwidth of 3.1 bits. In addition, we show that the learned bitwidths also generalize to other code rates and channels.

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arXiv2022

A Polar Subcode Approach to Belief Propagation List Decoding

Permutation decoding gained recent interest as it can exploit the symmetries of a code in a parallel fashion. Moreover, it has been shown that by viewing permuted polar codes as polar subcodes, the set of usable permutations in permutation decoding can be increased. We extend this idea to pre-transformed polar codes, such as cyclic redundancy check (CRC)-aided polar codes, which previously could not be decoded using permutations due to their lack of automorphisms. Using belief propagation (BP)-based subdecoders, we showcase a performance close to CRC-aided SCL (CA-SCL) decoding. The proposed algorithm outperforms the previously best performing iterative CRC-aided belief propagation list (CA-BPL) decoder both in error-rate performance and decoding latency.

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arXiv2022

Automorphism Ensemble Decoding of Quasi-Cyclic LDPC Codes by Breaking Graph Symmetries

We consider automorphism ensemble decoding (AED) of quasi-cyclic (QC) low-density parity-check (LDPC) codes. Belief propagation (BP) decoding on the conventional factor graph is equivariant to the quasi-cyclic automorphisms and therefore prevents gains by AED. However, by applying small modifications to the parity-check matrix at the receiver side, we can break the symmetry without changing the code at the transmitter. This way, we can leverage a gain in error-correcting performance using an ensemble of identical BP decoders, without increasing the worst-case decoding latency. The proposed method is demonstrated using LDPC codes from the CCSDS, 802.11n and 5G standards and produces gains of 0.2 to 0.3 dB over conventional BP decoding. Compared to the similarly performing saturated BP (SBP), the proposed algorithm reduces the average decoding latency by more than eight times.

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arXiv2021

Iterative Reed-Muller Decoding

Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an open problem. In this work, we present a belief propagation (BP) decoding architecture for RM codes based on their rich automorphism group. The decoding algorithm can be seen as a generalization of multiple-bases belief propagation (MBBP) using polar BP as constituent decoders. We provide extensive error-rate performance simulations and compare our results to existing decoding schemes. We report a near-ML performance for the RM(3,7)-code (e.g., 0.05 dB away from the ML bound at BLER of $10^{-4}$) at a competitive computational cost. To the best of our knowledge, our proposed decoder achieves the best performance of all iterative RM decoders presented thus far.

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arXiv2021

Automorphism Ensemble Decoding of Reed-Muller Codes

Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an open problem. In this work, we present a versatile decoding architecture for RM codes based on their rich automorphism group. The decoding algorithm can be seen as a generalization of multiple-bases belief propagation (MBBP) and may use any polar or RM decoder as constituent decoders. We provide extensive error-rate performance simulations for successive cancellation (SC)-, SC-list (SCL)- and belief propagation (BP)-based constituent decoders. We furthermore compare our results to existing decoding schemes and report a near-ML performance for the RM(3,7)-code (e.g., 0.04 dB away from the ML bound at BLER of $10^{-3}$) at a competitive computational cost. Moreover, we provide some insights into the automorphism subgroups of RM codes and SC decoding and, thereby, prove the theoretical limitations of this method with respect to polar codes.

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arXiv2021

On the Automorphism Group of Polar Codes

The automorphism group of a code is the set of permutations of the codeword symbols that map the whole code onto itself. For polar codes, only a part of the automorphism group was known, namely the lower-triangular affine group (LTA), which is solely based upon the partial order of the code's synthetic channels. Depending on the design, however, polar codes can have a richer set of automorphisms. In this paper, we extend the LTA to a larger subgroup of the general affine group (GA), namely the block lower-triangular affine group (BLTA) and show that it is contained in the automorphism group of polar codes. Furthermore, we provide a low complexity algorithm for finding this group for a given information/frozen set and determining its size. Most importantly, we apply these findings in automorphism-based decoding of polar codes and report a comparable error-rate performance to that of successive cancellation list (SCL) decoding with significantly lower complexity.

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arXiv2020

Iterative Detection and Decoding of Finite-Length Polar Codes in Gaussian Multiple Access Channels

We consider the usage of finite-length polar codes for the Gaussian multiple access channel (GMAC) with a finite number of users. Based on the interleave-division multipleaccess (IDMA) concept, we implement an iterative detection and decoding non-orthogonal multiple access (NOMA) receiver that benefits from a low complexity, while scaling (almost) linearly with the amount of active users. We further show the conceptual simplicity of the belief propagation (BP)-based decoder in a step-by-step illustration of its construction. Beyond its conceptual simplicity, this approach benefits from an improved performance when compared to some recent work tackling the same problem, namely the setup of finite-length forward errorcorrection (FEC) codes for finite-number of users. We consider the 5th generation mobile communication (5G) polar code with a block length $N = 512$ applied to both a two-user and a four-user GMAC scenario with a sum-rate of $R_{sum} = 0.5$ and $R_{sum} = 1$, respectively. Simulation results show that a BP-based soft interference cancellation (SoIC) receiver outperforms a joint successive cancellation (JSC) scheme. Finally, we investigate the effect of a concatenated repetition code which suggests that alternative polar code design rules are required in multi-user scenarios.

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arXiv2020

CRC-Aided Belief Propagation List Decoding of Polar Codes

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) 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).

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arXiv2019

Deep Learning-based Polar Code Design

In this work, we introduce a deep learning-based polar code construction algorithm. The core idea is to represent the information/frozen bit indices of a polar code as a binary vector which can be interpreted as trainable weights of a neural network (NN). For this, we demonstrate how this binary vector can be relaxed to a soft-valued vector, facilitating the learning process through gradient descent and enabling an efficient code construction. We further show how different polar code design constraints (e.g., code rate) can be taken into account by means of careful binary-to-soft and soft-to-binary conversions, along with rate-adjustment after each learning iteration. Besides its conceptual simplicity, this approach benefits from having the "decoder-in-the-loop", i.e., the nature of the decoder is inherently taken into consideration while learning (designing) the polar code. We show results for belief propagation (BP) decoding over both AWGN and Rayleigh fading channels with considerable performance gains over state-of-the-art construction schemes.

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arXiv2019

Optimizing Polar Codes Compatible with Off-the-Shelf LDPC Decoders

Previous work showed that polar codes can be decoded using off-the-shelf LDPC decoders by imposing special constraints on the LDPC code structure, which, however, resulted in some performance degradation. In this paper we show that this loss can be mitigated; in particular, we demonstrate how the gap between LDPC-style decoding and Arikan's Belief Propagation (BP) decoding of polar codes can be closed by taking into account the underlying graph structure of the LDPC decoder while jointly designing the polar code and the parity-check matrix of the corresponding LDPC-like code. The resulting polar codes under conventional LDPC-style decoding are shown to have similar error-rate performance when compared to some well-known and standardized LDPC codes. Moreover, we obtain performance gains in the high SNR region.

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arXiv2019

Decoder-in-the-Loop: Genetic Optimization-based LDPC Code Design

LDPC code design tools typically rely on asymptotic code behavior and are affected by an unavoidable performance degradation due to model imperfections in the short length regime. We propose an LDPC code design scheme based on an evolutionary algorithm, the Genetic Algorithm (GenAlg), implementing a "decoder-in-the-loop" concept. It inherently takes into consideration the channel, code length and the number of iterations while optimizing the error-rate of the actual decoder hardware architecture. We construct short length LDPC codes (i.e., the parity-check matrix) with error-rate performance comparable to, or even outperforming that of well-designed standardized short length LDPC codes over both AWGN and Rayleigh fading channels. Our proposed algorithm can be used to design LDPC codes with special graph structures (e.g., accumulator-based codes) to facilitate the encoding step, or to satisfy any other practical requirement. Moreover, GenAlg can be used to design LDPC codes with the aim of reducing decoding latency and complexity, leading to coding gains of up to $0.325$ dB and $0.8$ dB at BLER of $10^{-5}$ for both AWGN and Rayleigh fading channels, respectively, when compared to state-of-the-art short LDPC codes. Also, we analyze what can be learned from the resulting codes and, as such, the GenAlg particularly highlights design paradigms of short length LDPC codes (e.g., codes with degree-1 variable nodes obtain very good results).

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arXiv2019

Decoder-tailored Polar Code Design Using the Genetic Algorithm

We propose a new framework for constructing polar codes (i.e., selecting the frozen bit positions) for arbitrary channels, and tailored to a given decoding algorithm, rather than based on the (not necessarily optimal) assumption of successive cancellation (SC) decoding. The proposed framework is based on the Genetic Algorithm (GenAlg), where populations (i.e., collections) of information sets evolve successively via evolutionary transformations based on their individual error-rate performance. These populations converge towards an information set that fits both the decoding behavior and the defined channel. Using our proposed algorithm over the additive white Gaussian noise (AWGN) channel, we construct a polar code of length 2048 with code rate 0.5, without the CRC-aid, tailored to plain successive cancellation list (SCL) decoding, achieving the same error-rate performance as the CRC-aided SCL decoding, and leading to a coding gain of 1 dB at BER of $10^{-6}$. Further, a 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 total number of low-weight codewords. To demonstrate the flexibility, coding gains for the Rayleigh channel are shown under SCL and BP decoding. Besides improvements in error-rate performance, we show that, when required, the GenAlg can be also set up to reduce the decoding complexity, e.g., the SCL list size or the number of BP iterations can be reduced, while maintaining the same error-rate performance.

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arXiv2019

Genetic Algorithm-based Polar Code Construction for the AWGN Channel

We propose a new polar code construction framework (i.e., selecting the frozen bit positions) for the additive white Gaussian noise (AWGN) channel, tailored to a given decoding algorithm, rather than based on the (not necessarily optimal) assumption of successive cancellation (SC) decoding. The proposed framework is based on the Genetic Algorithm (GenAlg), where populations (i.e., collections) of information sets evolve successively via evolutionary transformations based on their individual error-rate performance. These populations converge towards an information set that fits the decoding behavior. Using our proposed algorithm, we construct a polar code of length 2048 with code rate 0.5, without the CRC-aid, tailored to plain successive cancellation list (SCL) decoding, achieving the same error-rate performance as the CRC-aided SCL decoding, and leading to a coding gain of 1 dB at BER of $10^{-6}$. Further, a belief propagation (BP)-tailored polar code approaches the SCL error-rate performance without any modifications in the decoding algorithm itself.

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arXiv2018

Belief Propagation List Decoding of Polar Codes

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 lower decoding latency compared to 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.

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arXiv2018

Sparse Graphs for Belief Propagation Decoding of Polar Codes

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.

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