arXiv subjects

Seyyed Ali Hashemi

Publications and source records attributed to Seyyed Ali Hashemi.

At least 19 recordsLinked to original sources

arXiv2023

Scalable Polar Code Construction for Successive Cancellation List Decoding: A Graph Neural Network-Based Approach

While constructing polar codes for successive-cancellation decoding can be implemented efficiently by sorting the bit-channels, finding optimal polar codes for cyclic-redundancy-check-aided successive-cancellation list (CA-SCL) decoding in an efficient and scalable manner still awaits investigation. This paper first maps a polar code to a unique heterogeneous graph called the polar-code-construction message-passing (PCCMP) graph. Next, a heterogeneous graph-neural-network-based iterative message-passing (IMP) algorithm is proposed which aims to find a PCCMP graph that corresponds to the polar code with minimum frame error rate under CA-SCL decoding. This new IMP algorithm's major advantage lies in its scalability power. That is, the model complexity is independent of the blocklength and code rate, and a trained IMP model over a short polar code can be readily applied to a long polar code's construction. Numerical experiments show that IMP-based polar-code constructions outperform classical constructions under CA-SCL decoding. In addition, when an IMP model trained on a length-128 polar code directly applies to the construction of polar codes with different code rates and blocklengths, simulations show that these polar code constructions deliver comparable performance to the 5G polar codes.

cs.IT↗

arXiv2022

Decoding Reed-Muller Codes with Successive Codeword Permutations

A novel recursive list decoding (RLD) algorithm for Reed-Muller (RM) codes based on successive permutations (SP) of the codeword is presented. A low-complexity SP scheme applied to a subset of the symmetry group of RM codes is first proposed to carefully select a good codeword permutation on the fly. Then, the proposed SP technique is integrated into an improved RLD algorithm that initializes different decoding paths with random codeword permutations, which are sampled from the full symmetry group of RM codes. Finally, efficient latency and complexity reduction schemes are introduced that virtually preserve the error-correction performance of the proposed decoder. Simulation results demonstrate that at the target frame error rate of $10^{-3}$ for the RM code of length $256$ with $163$ information bits, the proposed decoder reduces $6\%$ of the computational complexity and $22\%$ of the decoding latency of the state-of-the-art semi-parallel simplified successive-cancellation decoder with fast Hadamard transform (SSC-FHT) that uses $96$ permutations from the full symmetry group of RM codes, while relatively maintaining the error-correction performance and memory consumption of the semi-parallel permuted SSC-FHT decoder.

cs.IT↗

arXiv2022

Successive-Cancellation Decoding of Reed-Muller Codes with Fast Hadamard Transform

A novel permuted fast successive-cancellation list decoding algorithm with fast Hadamard transform (FHT-FSCL) is presented. The proposed decoder initializes $L$ $(L\ge1)$ active decoding paths with $L$ random codeword permutations sampled from the full symmetry group of the codes. The path extension in the permutation domain is carried out until the first constituent RM code of order $1$ is visited. Conventional path extension of the successive-cancellation list decoder is then utilized in the information bit domain. The simulation results show that for a RM code of length $512$ with $46$ information bits, by running $20$ parallel permuted FHT-FSCL decoders with $L=4$, we reduce $72\%$ of the computational complexity, $22\%$ of the decoding latency, and $84\%$ of the memory consumption of the state-of-the-art simplified successive-cancellation decoder that uses $512$ permutations sampled from the full symmetry group of the code, with similar error-correction performance at the target frame error rate of $10^{-4}$.

cs.IT↗

arXiv2022

Fast Successive-Cancellation List Flip Decoding of Polar Codes

This work presents a fast successive-cancellation list flip (Fast-SCLF) decoding algorithm for polar codes that addresses the high latency issue associated with the successive-cancellation list flip (SCLF) decoding algorithm. We first propose a bit-flipping strategy tailored to the state-of-the-art fast successive-cancellation list (FSCL) decoding that avoids tree-traversal in the binary tree representation of SCLF, thus reducing the latency of the decoding process. We then derive a parameterized path selection error model to accurately estimate the bit index at which the correct decoding path is eliminated from the initial FSCL decoding. The trainable parameter is optimized online based on an efficient supervised learning framework. Simulation results show that for a polar code of length 512 with 256 information bits, with similar error-correction performance and memory consumption, the proposed Fast-SCLF decoder reduces up to $73.4\%$ of the average decoding latency of the SCLF decoder with the same list size at the frame error rate of $10^{-4}$, while incurring a maximum computational complexity overhead of $27.6\%$. For the same polar code of length 512 with 256 information bits and at practical signal-to-noise ratios, the proposed decoder with list size 4 reduces $89.3\%$ and $43.7\%$ of the average complexity and decoding latency of the FSCL decoder with list size 32 (FSCL-32), respectively, while also reducing $83.2\%$ of the memory consumption of FSCL-32. The significant improvements of the proposed decoder come at the cost of $0.07$ dB error-correction performance degradation compared with FSCL-32.

cs.IT↗

arXiv2021

Successive Syndrome-Check Decoding of Polar Codes

A two-part successive syndrome-check decoding of polar codes is proposed with the first part successively refining the received codeword and the second part checking its syndrome. A new formulation of the successive-cancellation (SC) decoding algorithm is presented that allows for successively refining the received codeword by comparing the log-likelihood ratio value of a frozen bit with its predefined value. The syndrome of the refined received codeword is then checked for possible errors. In case there are no errors, the decoding process is terminated. Otherwise, the decoder continues to refine the received codeword. The proposed method is extended to the case of SC list (SCL) decoding by terminating the decoding process when the syndrome of the best candidate in the list indicates no errors. Simulation results show that the proposed method reduces the time-complexity of SC and SCL decoders and their fast variants, especially at high signal-to-noise ratios.

cs.IT↗

arXiv2021

A Tree Search Approach for Maximum-Likelihood Decoding of Reed-Muller Codes

A low-complexity tree search approach is presented that achieves the maximum-likelihood (ML) decoding performance of Reed-Muller (RM) codes. The proposed approach generates a bit-flipping tree that is traversed to find the ML decoding result by performing successive-cancellation decoding after each node visit. A depth-first search (DFS) and a breadth-first search (BFS) scheme are developed and a log-likelihood-ratio-based bit-flipping metric is utilized to avoid redundant node visits in the tree. Several enhancements to the proposed algorithm are presented to further reduce the number of node visits. Simulation results confirm that the BFS scheme provides a lower average number of node visits than the existing tree search approach to decode RM codes.

cs.IT↗

arXiv2020

Parallelism versus Latency in Simplified Successive-Cancellation Decoding of Polar Codes

This paper characterizes the latency of the simplified successive-cancellation (SSC) decoding scheme for polar codes under hardware resource constraints. In particular, when the number of processing elements $P$ that can perform SSC decoding operations in parallel is limited, as is the case in practice, the latency of SSC decoding is $O\left(N^{1-1/μ}+\frac{N}{P}\log_2\log_2\frac{N}{P}\right)$, where $N$ is the block length of the code and $μ$ is the scaling exponent of the channel. Three direct consequences of this bound are presented. First, in a fully-parallel implementation where $P=\frac{N}{2}$, the latency of SSC decoding is $O\left(N^{1-1/μ}\right)$, which is sublinear in the block length. This recovers a result from our earlier work. Second, in a fully-serial implementation where $P=1$, the latency of SSC decoding scales as $O\left(N\log_2\log_2 N\right)$. The multiplicative constant is also calculated: we show that the latency of SSC decoding when $P=1$ is given by $\left(2+o(1)\right) N\log_2\log_2 N$. Third, in a semi-parallel implementation, the smallest $P$ that gives the same latency as that of the fully-parallel implementation is $P=N^{1/μ}$. The tightness of our bound on SSC decoding latency and the applicability of the foregoing results is validated through extensive simulations.

cs.IT↗

arXiv2020

Threshold-Based Fast Successive-Cancellation Decoding of Polar Codes

Fast SC decoding overcomes the latency caused by the serial nature of the SC decoding by identifying new nodes in the upper levels of the SC decoding tree and implementing their fast parallel decoders. In this work, we first present a novel sequence repetition node corresponding to a particular class of bit sequences. Most existing special node types are special cases of the proposed sequence repetition node. Then, a fast parallel decoder is proposed for this class of node. To further speed up the decoding process of general nodes outside this class, a threshold-based hard-decision-aided scheme is introduced. The threshold value that guarantees a given error-correction performance in the proposed scheme is derived theoretically. Analysis and hardware implementation results on a polar code of length $1024$ with code rates $1/4$, $1/2$, and $3/4$ show that our proposed algorithm reduces the required clock cycles by up to $8\%$, and leads to a $10\%$ improvement in the maximum operating frequency compared to state-of-the-art decoders without tangibly altering the error-correction performance. In addition, using the proposed threshold-based hard-decision-aided scheme, the decoding latency can be further reduced by $57\%$ at $\mathrm{E_b}/\mathrm{N_0} = 5.0$~dB.

cs.IT↗

arXiv2020

Sparse Multi-Decoder Recursive Projection Aggregation for Reed-Muller Codes

Reed-Muller (RM) codes are one of the oldest families of codes. Recently, a recursive projection aggregation (RPA) decoder has been proposed, which achieves a performance that is close to the maximum likelihood decoder for short-length RM codes. One of its main drawbacks, however, is the large amount of computations needed. In this paper, we devise a new algorithm to lower the computational budget while keeping a performance close to that of the RPA decoder. The proposed approach consists of multiple sparse RPAs that are generated by performing only a selection of projections in each sparsified decoder. In the end, a cyclic redundancy check (CRC) is used to decide between output codewords. Simulation results show that our proposed approach reduces the RPA decoder's computations up to $80\%$ with negligible performance loss.

cs.IT↗

arXiv2020

Construction of Polar Codes with Reinforcement Learning

This paper formulates the polar-code construction problem for the successive-cancellation list (SCL) decoder as a maze-traversing game, which can be solved by reinforcement learning techniques. The proposed method provides a novel technique for polar-code construction that no longer depends on sorting and selecting bit-channels by reliability. Instead, this technique decides whether the input bits should be frozen in a purely sequential manner. The equivalence of optimizing the polar-code construction for the SCL decoder under this technique and maximizing the expected reward of traversing a maze is drawn. Simulation results show that the standard polar-code constructions that are designed for the successive-cancellation decoder are no longer optimal for the SCL decoder with respect to the frame error rate. In contrast, the simulations show that, with a reasonable amount of training, the game-based construction method finds code constructions that have lower frame-error rate for various code lengths and decoders compared to standard constructions.

cs.IT↗

arXiv2020

Decoding Polar Codes with Reinforcement Learning

In this paper we address the problem of selecting factor-graph permutations of polar codes under belief propagation (BP) decoding to significantly improve the error-correction performance of the code. In particular, we formalize the factor-graph permutation selection as the multi-armed bandit problem in reinforcement learning and propose a decoder that acts like an online-learning agent that learns to select the good factor-graph permutations during the course of decoding. We use state-of-the-art algorithms for the multi-armed bandit problem and show that for a 5G polar codes of length 128 with 64 information bits, the proposed decoder has an error-correction performance gain of around 0.125 dB at the target frame error rate of 10^{-4}, when compared to the approach that randomly selects the factor-graph permutations.

cs.IT↗

arXiv2020

Sublinear Latency for Simplified Successive Cancellation Decoding of Polar Codes

This work analyzes the latency of the simplified successive cancellation (SSC) decoding scheme for polar codes proposed by Alamdar-Yazdi and Kschischang. It is shown that, unlike conventional successive cancellation decoding, where latency is linear in the block length, the latency of SSC decoding is sublinear. More specifically, the latency of SSC decoding is $O(N^{1-1/μ})$, where $N$ is the block length and $μ$ is the scaling exponent of the channel, which captures the speed of convergence of the rate to capacity. Numerical results demonstrate the tightness of the bound and show that most of the latency reduction arises from the parallel decoding of subcodes of rate $0$ or $1$.

cs.IT↗

arXiv2019

Deep-Learning-Aided Successive-Cancellation Decoding of Polar Codes

A deep-learning-aided successive-cancellation list (DL-SCL) decoding algorithm for polar codes is introduced with deep-learning-aided successive-cancellation (DL-SC) decoding being a specific case of it. The DL-SCL decoder works by allowing additional rounds of SCL decoding when the first SCL decoding attempt fails, using a novel bit-flipping metric. The proposed bit-flipping metric exploits the inherent relations between the information bits in polar codes that are represented by a correlation matrix. The correlation matrix is then optimized using emerging deep-learning techniques. Performance results on a polar code of length 128 with 64 information bits concatenated with a 24-bit cyclic redundancy check show that the proposed bit-flipping metric in the proposed DL-SCL decoder requires up to 66% fewer multiplications and up to 36% fewer additions, without any need to perform transcendental functions, and by providing almost the same error-correction performance in comparison with the state of the art.

cs.IT↗

arXiv2019

Efficient Flicker-Free FEC Codes using Knuth's Balancing Algorithm for VLC

Visible light communication (VLC) provides a short-range optical wireless communication through light-emitting diode (LED) lighting. Light beam flickering and dimming are among the challenges to be addressed in VLC. Conventional methods for generating flicker-free codes in VLC are based on run-length limited codes that have poor error correction performance, use lookup tables which are memory consuming, and have low transmission rates. In this paper, we propose an efficient construction of flicker-free forward error correction codes to tackle the issue of flickering in VLC. Our simulation results show that by using polar codes and at a dimming ratio of 50%, the proposed system generates flicker-free codes without using lookup tables, while having lower complexity and higher transmission rates than the standard VLC methods. For an information block length of 256, the error correction performance of the proposed scheme is $1.8$ dB and $0.9$ dB better than that of the regular schemes at the bit error rate of $10^{-6}$ for a rate of 0.44 and 0.23, respectively.

cs.IT↗

arXiv2019

Neural Dynamic Successive Cancellation Flip Decoding of Polar Codes

Dynamic successive cancellation flip (DSCF) decoding of polar codes is a powerful algorithm that can achieve the error correction performance of successive cancellation list (SCL) decoding, with a complexity that is close to that of successive cancellation (SC) decoding at practical signal-to-noise ratio (SNR) regimes. However, DSCF decoding requires costly transcendental computations which adversely affect its implementation complexity. In this paper, we first show that a direct application of common approximation schemes on the conventional DSCF decoding results in significant error-correction performance loss. We then introduce a training parameter and propose an approximation scheme which completely removes the need to perform transcendental computations in DSCF decoding, with almost no error-correction performance degradation.

cs.IT↗

arXiv2019

Rate-Flexible Fast Polar Decoders

Polar codes have gained extensive attention during the past few years and recently they have been selected for the next generation of wireless communications standards (5G). Successive-cancellation-based (SC-based) decoders, such as SC list (SCL) and SC flip (SCF), provide a reasonable error performance for polar codes at the cost of low decoding speed. Fast SC-based decoders, such as Fast-SSC, Fast-SSCL, and Fast-SSCF, identify the special constituent codes in a polar code graph off-line, produce a list of operations, store the list in memory, and feed the list to the decoder to decode the constituent codes in order efficiently, thus increasing the decoding speed. However, the list of operations is dependent on the code rate and as the rate changes, a new list is produced, making fast SC-based decoders not rate-flexible. In this paper, we propose a completely rate-flexible fast SC-based decoder by creating the list of operations directly in hardware, with low implementation complexity. We further propose a hardware architecture implementing the proposed method and show that the area occupation of the rate-flexible fast SC-based decoder in this paper is only $38\%$ of the total area of the memory-based base-line decoder when 5G code rates are supported.

cs.IT↗

arXiv2018

Neural Belief Propagation Decoding of CRC-Polar Concatenated Codes

Polar codes are the first class of error correcting codes that provably achieve the channel capacity at infinite code length. They were selected for use in the fifth generation of cellular mobile communications (5G). In practical scenarios such as 5G, a cyclic redundancy check (CRC) is concatenated with polar codes to improve their finite length performance. This is mostly beneficial for sequential successive-cancellation list decoders. However, for parallel iterative belief propagation (BP) decoders, CRC is only used as an early stopping criterion with incremental error-correction performance improvement. In this paper, we first propose a CRC-polar BP (CPBP) decoder by exchanging the extrinsic information between the factor graph of the polar code and that of the CRC. We then propose a neural CPBP (NCPBP) algorithm which improves the CPBP decoder by introducing trainable normalizing weights on the concatenated factor graph. Our results on a 5G polar code of length 128 show that at the frame error rate of 10^(-5) and with a maximum of 30 iterations, the error-correction performance of CPBP and NCPBP are approximately 0.25 dB and 0.5 dB better than that of the conventional CRC-aided BP decoder, respectively, while introducing almost no latency overhead.

cs.IT↗

arXiv2018

Partitioned Successive-Cancellation Flip Decoding of Polar Codes

Polar codes are a class of channel capacity achieving codes that has been selected for the next generation of wireless communication standards. Successive-cancellation (SC) is the first proposed decoding algorithm, suffering from mediocre error-correction performance at moderate code length. In order to improve the error-correction performance of SC, two approaches are available: (i) SC-List decoding which keeps a list of candidates by running a number of SC decoders in parallel, thus increasing the implementation complexity, and (ii) SC-Flip decoding that relies on a single SC module, and keeps the computational complexity close to SC. In this work, we propose the partitioned SC-Flip (PSCF) decoding algorithm, which outperforms SC-Flip in terms of error-correction performance and average computational complexity, leading to higher throughput and reduced energy consumption per codeword. We also introduce a partitioning scheme that best suits our PSCF decoder. Simulation results show that at equivalent frame error rate, PSCF has up to $5 \times$ less computational complexity than the SC-Flip decoder. At equivalent average number of iterations, the error-correction performance of PSCF outperforms SC-Flip by up to $0.15$ dB at frame error rate of $10^{-3}$.

cs.IT↗