Computational Complexity Of Decoder Research Articles

SparseDet: Towards efficient multi-view 3D object detection via sparse scene representation

Efficient and reliable 3D object detection via multi-view cameras is pivotal for improving the safety and facilitating the cost-effective deployment of autonomous driving systems. However, owing to the learning of dense scene representations, existing methods still suffer from high computational costs and excessive noise, affecting the efficiency and accuracy of the inference process. To overcome this challenge, we propose SparseDet, a model that exploits sparse scene representations. Specifically, a sparse sampling module with category-aware and geometry-aware supervision is first introduced to adaptively sample foreground features at both semantic and instance levels. Additionally, to conserve computational resources while retaining context information, we propose a background aggregation module designed to compress extensive background features into a compact set. These strategies can markedly diminish feature volume while preserving essential information to boost computational efficiency without compromising accuracy. Due to the efficient sparse scene representation, our SparseDet achieves leading performance on the widely used nuScenes benchmark. Comprehensive experiments validate that SparseDet surpasses the PETR while reducing the decoder computational complexity by 47% in terms of FLOPs, facilitating a leading inference speed of 35.6 FPS on a single RTX3090 GPU.

Application of Guessing to Sequential Decoding of Polarization-Adjusted Convolutional (PAC) Codes

Despite the extreme error-correction performance, the amount of computation of sequential decoding of the polarization-adjusted convolutional (PAC) codes is random. In sequential decoding of convolutional codes, the cutoff rate denotes the region between rates whose average computational complexity of decoding is finite and those which is infinite. In this paper, by benefiting from the polarization and guessing techniques, we prove that the required computation in sequential decoding of pre-transformed polar codes polarizes, and this polarization determines which set of bit positions within the rate profile may result in high computational complexity. Based on this, we propose a technique for taming the Reed-Muller (RM) rate-profile construction, and the performance results demonstrate that the error-correction performance of the PAC codes can achieve the theoretical bounds using the tamed-RM rate-profile construction and requires a significantly lower computational complexity than the RM rate-profile construction.

Gated fusion network for SAO filter and inter frame prediction in Versatile Video Coding

In order to achieve higher coding efficiency, the Versatile Video Coding (VVC) standard includes several new components at the expense of an increase in decoder computational complexity. These technologies often create ringing and contouring effects on the reconstructed frames at a low bit rate and introduce blurring and distortion. To smooth those visual artifacts, the H.266/VVC framework supports four post-processing filter operations. The state-of-the-art CNN-based in-loop filters prefer to deploy multiple networks for various quantization parameters and frame resolutions, which increases training resources and subsequently becomes overhead at decoder frame reconstruction. This paper presents a single deep-learning-based model for sample adaptive off-set (SAO) non-linear filtering operation on the decoder side, uses feature correlation among adjacent frames, and substantiates the merits of intra–inter frame quality enhancement. We introduced a variable filter size dual multi-scale convolutional neural network (D-MSCNN) to attenuate the compression artifact and incorporated strided deconvolution to restore the high-frequency details on the distorted frame. Our model follows sequential training across all QP values and updates the model weights. Using data augmentation, weight fusion, and residual learning, we demonstrated that our model could be trained effectively by transferring the convolution prior feature indices to the decoder to produce a dense output map. The Objective measurements demonstrate that the proposed method outperforms the baseline VVC method in PSNR, MS-SSIM, and VMAF metrics and achieves an average of 5.16% bit rate saving on different test sequence categories.

СИНТЕЗ СПЕКТРАЛЬНО ТА ЕНЕРГЕТИЧНО-ЕФЕКТИВНИХ СИГНАЛЬНО-КОДОВИХ КОНСТРУКЦІЙ ДЛЯ СИСТЕМ МІМО З ПРОСТОРОВИМ КОДУВАННЯМ СИГНАЛІВ

Wireless communication systems are considered, the main task of which is to increase their spectral (SE) and energy efficiency (EE) in conditions of limited frequency and energy resources. Additional use of the spatial resource based on flexible and universal methods of signals Space-Time Coding (STC) in MIMO-systems (Multiple Input - Multiple Output) can significantly increase the SE and EE values, as well as significantly improve the capabilities and conditions for EE exchange on SE. The advantages and disadvantages of Orthogonal Space-Time Block Coding (OSTBC) and Non-Orthogonal STBC (NOSTBC) are shown. Two main methods of synthesis of spectrally and energy-efficient information transmission methods are demonstrated. The first method is implemented by creating Perfect-codes that simultaneously achieve maximum diversity and multiplexing gains. The exponential computational decoding complexity of such codes makes it impossible for their practical implementation in mobile terminals at the present stage of development of circuitry. The second method of synthesis is based on improving the simple basic STC methods in terms of increasing the SE and EE by creating Signal-Code Constructions (SCC), which have the advantages of the basic STC methods and are devoid of the disadvantages inherent in Perfect-codes. A technique for the synthesis of SCC is proposed, the essence of which is to determine the priority areas (by the value of the Signal-to-Noise Ratio (SNR)) of using the STC and corresponding signal constellations, which provide the maximum SE for a guaranteed Bit Error Rate (BER). It was found that MIMO 2x2 with Alamouti OSTBC has an advantage in terms of EE over NOSTBC type VBLAST for SE not more than 8 b/s/Hz and SNR under 35 dB, BER not exceeding 10-5. In MIMO 4x4, OSTBC codes are inferior to NOSTBC in terms of EE. VBLAST code allows to provide SE 4 - 8 b/s/Hz at SNR 10 - 20 dB, BER not exceeding 10-5. Based on the results obtained, propositions for further improvement of OSTBC and NOSTBC are formulated.

An Improved BP Decoding of BATS Codes With Iterated Incremental Gaussian Elimination

In this letter, we propose an improved algorithm for decoding finite-length BATS codes using belief propagation (BP) decoding. Our proposed algorithm iteratively performs BP decoding and incremental Gaussian elimination for improving the decoding performance. Furthermore, instead of directly using Gaussian elimination after BP decoding, the incremental Gaussian elimination has been iteratively used to resume BP decoding, which can noticeably reduce the computational complexity of decoding. The simulation results demonstrate that the proposed decoding algorithm can achieve the same decoding performance as conventional Gaussian elimination while significantly reducing the number of finite field operations in decoding.

Hamming–Luby rateless codes for molecular erasure channels

Nano-scale molecular communications encode digital information into discrete macro-molecules. In many nano-scale systems, due to limited molecular energy, each information symbol is encoded into a small number of molecules. As such, information may be lost in the process of diffusion–advection propagation through complex topologies and membranes. Existing Hamming-distance codes for additive counting noise are not well suited to combat the aforementioned erasure errors. Rateless Luby-Transform (LT) code and cascaded Hamming-LT (Raptor) are suitable for information-loss, however may consume substantially computational energy due to the repeated uses of random number generator and exclusive OR (XOR). In this paper, we design a novel low-complexity erasure combating encoding scheme: the rateless Hamming–Luby Transform code. The proposed rateless code combines the superior efficiency of Hamming codes with the performance guarantee advantage of Luby Transform (LT) codes, therefore can reduce the number of random number generator utilizations. We design an iterative soft decoding scheme via successive cancelation to further improve the performance. Numerical simulations show this new rateless code can provide comparable performance comparing with both standard LT and Raptor codes, while incurring a lower decoder computational complexity, which is useful for the envisaged resources constrained nano-machines.

A 2.267-Gb/s, 93.7-pJ/bit Non-Binary LDPC Decoder With Logarithmic Quantization and Dual-Decoding Algorithm Scheme for Storage Applications

Non-binary low-density parity-check (NB-LDPC) codes are a promising class of error-correcting codes that provide excellent coding gain beyond that of their binary counterparts. However, their decoding complexity has thus far limited practicality. We present an NB-LDPC decoder with information throughput of 2.267 Gb/s and power consumption of 212.4 mW, yielding an energy efficiency of 93.7 pJ/bit, implemented in 40-nm CMOS technology. The employed code is long and high-rate without degree-2 variable nodes, resulting in a low error floor and making the code appropriate for storage applications. A logarithmic quantization scheme is proposed to enable aggressive wordlength reduction to alleviate hardware complexity. In addition, a dual-decoding algorithm scheme is employed to alleviate the computational complexity of decoding, realized in an efficient architecture with high parallelism and avoidance of idle clock cycles.

Fast Decoding of Dual Multipoint Codes From Algebraic Curves Up to the Kirfel–Pellikaan Bound

The multipoint codes from algebraic curves are a broad class of algebraic geometry codes derived from algebraic functions, which have multiple poles/zeros on their defining curves. Each of them is defined as either a primal code or a dual code. The dual one-point codes which are viewed as a subclass can be decoded efficiently up to the Feng–Rao bound by using the Berlekamp–Massey–Sakata (BMS) algorithm with majority logic. Since a primal code is equivalent to a dual code, one can decode as either of them, while their decoding methods are different. Recently, we published a fast method for decoding primal multipoint codes from curves based on the vectorial BMS algorithm. But, that is neither for dual codes nor up to the Goppa bound $d_{\mathrm{ Goppa}}$ . Although we can guarantee theoretically that every error vector of weight only up to $({1}/{2})(d_{\mathrm{ Goppa}}-g)$ can be corrected, where the integer $g$ is the genus of the defining curve, the simulation shows that the method can correct most error patterns of weight up to $({1}/{2})d_{\mathrm{ Goppa}}$ . In this paper we present a fast method for decoding dual multipoint codes from algebraic curves up to the Kirfel–Pellikaan bound, based on the vectorial BMS algorithm with majority logic, and show that algebraic geometry codes from generic algebraic curves can be decoded up to the Goppa bound efficiently. Similar to the case of one-point codes, the computational complexity of decoding is ${\mathcal{ O}}(a_{1}n^{2})$ , where the integer $a_{1}$ is the minimum nonzero pole order of algebraic functions on the defining curve and the integer $n$ is the code length, and in particular, ${\mathcal{ O}}(n^{({7}/{3})})$ for Hermitian codes. This complexity is less than the complexity ${\mathcal{ O}}(a_{1}gn^{2})$ of Lee’s method for decoding dual multipoint codes as a unique alternative.

Adaptive Compressive Sensing of Images Using Spatial Entropy.

Compressive Sensing (CS) realizes a low-complex image encoding architecture, which is suitable for resource-constrained wireless sensor networks. However, due to the nonstationary statistics of images, images reconstructed by the CS-based codec have many blocking artifacts and blurs. To overcome these negative effects, we propose an Adaptive Block Compressive Sensing (ABCS) system based on spatial entropy. Spatial entropy measures the amount of information, which is used to allocate measuring resources to various regions. The scheme takes spatial entropy into consideration because rich information means more edges and textures. To reduce the computational complexity of decoding, a linear mode is used to reconstruct each block by the matrix-vector product. Experimental results show that our ABCS coding system provides a better reconstruction quality from both subjective and objective points of view, and it also has a low decoding complexity.

Video Error Correction Using Soft-Output and Hard-Output Maximum Likelihood Decoding Applied to an H.264 Baseline Profile

Error concealment has long been identified as the last line of defense against transmission errors. Since error handling is outside the scope of video coding standards, decoders may choose to simply ignore corrupted packets or attempt to decode their content. In this paper, we present a novel joint source-channel decoding approach that can be applied to received video packets containing transmission errors. Soft-output information is combined with our novel syntax-element-level maximum likelihood decoding framework to effectively extract valid macroblocks from corrupted H.264 slices. Simulation results show that our video error correction strategy provides an average peak signal-to-noise ratio (PSNR) improvement near 2 dB compared to the error concealment approach used by the H.264 reference software, as well as an average PSNR improvement of 0.8 dB compared to state-of-the-art error concealment. The proposed method is also applicable when only hard-information is available, in which case it performs better than state-of-the-art error concealment especially in high error conditions. Finally, in our simulations, the proposed method increased the decoder computational complexity by only 5% to 20%, making it applicable for real-time applications.

Hybrid Distributed Correlation Noise Model and Parameter Estimation

In transform domain distributed video coding scheme, we found that there was a certain deviation between Laplacian statistical distribution and the distribution of small and large residual coefficients. To reduce this deviation, this paper proposes a hybrid distribution correlation noise model (HDCNM) based on K-Mediods, which models small coefficients as improved Laplacian distribution while modeling large ones as Cauchy distribution. The parameter estimation algorithm is also given. The experimental results show that the hybrid model proposed in this paper can describe the distribution of residual coefficients between WZ frame and side information accurately, so as to improve the distortion performance of transform domain distributed video coding effectively, and reduce the computational complexity of decoder.

A new computational decoding complexity measure of convolutional codes

Abstract This paper presents a computational complexity measure of convolutional codes well suitable for software implementations of the Viterbi algorithm (VA) operating with hard decision. We investigate the number of arithmetic operations performed by the decoding process over the conventional and minimal trellis modules. A relation between the complexity measure defined in this work and the one defined by McEliece and Lin is investigated. We also conduct a refined computer search for good convolutional codes (in terms of distance spectrum) with respect to two minimal trellis complexity measures. Finally, the computational cost of implementation of each arithmetic operation is determined in terms of machine cycles taken by its execution using a typical digital signal processor widely used for low-power telecommunications applications.

Geosphere

This paper presents the design and implementation of Geosphere, a physical- and link-layer design for access point-based MIMO wireless networks that consistently improves network throughput. To send multiple streams of data in a MIMO system, prior designs rely on a technique called zero-forcing, a way of "nulling" the interference between data streams by mathematically inverting the wireless channel matrix. In general, zero-forcing is highly effective, significantly improving throughput. But in certain physical situations, the MIMO channel matrix can become "poorly conditioned," harming performance. With these situations in mind, Geosphere uses sphere decoding, a more computationally demanding technique that can achieve higher throughput in such channels. To overcome the sphere decoder's computational complexity when sending dense wireless constellations at a high rate, Geosphere introduces search and pruning techniques that incorporate novel geometric reasoning about the wireless constellation. These techniques reduce computational complexity of 256-QAM systems by almost one order of magnitude, bringing computational demands in line with current 16- and 64-QAM systems already realized in ASIC. Geosphere thus makes the sphere decoder practical for the first time in a 4 × 4 MIMO, 256-QAM system. Results from our WARP testbed show that Geosphere achieves throughput gains over multi-user MIMO of 2× in 4 × 4 systems and 47% in 2 × 2 MIMO systems.

On the average complexity of sphere decoding in lattice space–time coded multiple‐input multiple‐output channel

AbstractThe exact average complexity analysis of the basic sphere decoder for general space–time codes applied to multiple‐input multiple‐output (MIMO) wireless channel is known to be difficult. In this work, we shed the light on the computational complexity of sphere decoding for the quasi‐static, lattice space–time (LAST) coded MIMO channel. Specifically, we drive an upper bound of the tail distribution of the decoder's computational complexity. We show that when the computational complexity exceeds a certain limit, this upper bound becomes dominated by the outage probability achieved by LAST coding and sphere decoding schemes. We then calculate the minimum average computational complexity that is required by the decoder to achieve near optimal performance in terms of the system parameters. Our results indicate that there exists a cut‐off rate (multiplexing gain) for which the average complexity remains bounded.Copyright © 2012 John Wiley & Sons, Ltd.

HEVC에서 인코더 계산 복잡도 개선 및 분할 정보 부호화 방법

본 논문에서는 참조 프레임 혹은 시간적으로 이전에 부호화한 프레임을 통해 현재 프레임의 LCU 분할구조를 예측하여 부호화하는 방법을 제안한다. HEVC에서는 CU로 부호화 및 복호화를 수행하는데, CU의 기본이 되는 LCU 단위로 영상의 특성에 따라 분할구조를 결정하여 영상을 적응적으로 부호화한다. 이 때, 현재 부호화하려는 LCU의 분할구조와 참조 프레임 및 시간적으로 이전에 부호화한 프레임 내의 동일한 위치에 대응되는 LCU(Co-located LCU)의 분할구조는 매우 유사한 특성이 있다. 따라서 본 논문에서는 인코더의 복잡도를 낮추기 위하여 현재 LCU의 분할구조를 결정할 때, Co-located LCU의 복잡성을 통해 현재 부호화하는 LCU의 분할구조 정보를 예측하고 분할구조에 포함될 확률이 높은 CU만 부호화하는 방법을 제안한다. 제안 방법의 시뮬레이션 결과로서, 인코더만을 변경하여 인코더 복잡도를 낮추는 방법이 기존 대비 인코더 복잡도가 평균 21.3% 감소하였고, 디코더 복잡도는 거의 비슷했으며, BD-Bitrate는 최대 0.6% 증가하였다. 또한 인코더에서 분할구조를 결정할 때 LCU의 분할 정보를 예측하여 부호화하고, CU 분할 정보를 부호화 및 복호화하는 과정을 변경하는 방법을 통해 BD-Bitrate를 감소시키는 방법을 제안하였다. 제안 방법의 시뮬레이션 결과는 인코더 복잡도가 평균 22% 감소하였고, 디코더 복잡도는 거의 비슷했으며, BD-Bitrate는 최대 0.3% 정도만 증가하여 제안하는 방법의 우수함을 확인할 수 있었다. This paper proposes the coding method to predict the split structure of LCU in the current frame on the basis of the reference frame or temporally-previous frame. HEVC encoder determines split structure according to image characteristics in LCU which is an basic element of CU. The split structure of the current LCU is very similar to the split structure of collocated LCU in the reference frame or temporally-previous frame. Thus, this paper proposes the method to reduce the encoder computational complexity by predicting split structure of the current LCU on the basis of that of collocated LCU in the reference frame or temporally-previous frame. And it also proposes the method to reduce the BD-Bitrate by coding after the prediction of the CU split information. The simulation results of changing only encoder showed that the mean of encoder computational complexity was lower by 21.3%, the decoder computational complexity was negligible change and the BD-Bitrate increase by the maximum of 0.6%. Also, the method changing encoder, bitstream, and decoder improves the mean of encoder computational complexity was lower by 22%, the decoder computational complexity was negligible change and the BD-Bitrate is improved to the maximum of 0.3%. When compared with the conventional method, indicating that the proposed method is superior.

HEVC를 위한 CU기반 병합 후보 리스트 구성 방법

본 논문에서는 기존 PU기반 움직임 병합 후보 리스트 생성 방법과 비교하여 계산 복잡도를 감소시키고 개선된 병렬성을 제공하기 위하여 CU 기반의 움직임 병합 후보 리스트 생성 방법을 제안한다. 제안하는 방법에서 하나의 CU는 오직 하나의 움직임 병합 후보 리스트를 생성한다. 그래서 CU내의 모든 PU 블록은 PU형태에 관계없이 오직 하나의 공통 움직임 병합 후보 리스트를 사용한다. 제안방법의 실험 결과, 기존 방법보다 인코더의 복잡도는 3% ~ 6% 감소하였으며, 디코더의 복잡도는 거의 변화가 없었다. 반면 제안 방법이 기존 방법보다 부호화 효율이 0.2% - 0.5% 감소된다는 단점이 존재한다. 하지만 제안방법은 하드웨어 구현이 간단하며, 계산 복잡도를 감소시키고 향상된 병렬성을 제공한다는 장점을 갖는다. This paper proposes the CU-based approach for merge candidate list construction for providing reduced complexity and improved parallelism compared to the PU-based one. In the proposed method, a CU can have only one merge candidate list. So, Only one common merge candidate list is used for all PUs in a CU regardless of the PU partition type. The simulation results of proposed method showed that the encoder computational complexity was decreased by 3% to 6% and the decoder computational complexity was negligible change with the penalty of roughly 0.2% - 0.5% coding loss. The proposed method has several advantages: it provides simpler design, reduced complexity, and improved parallelism.

An Efficient Viterbi Decoder

Convolutional encoding with Viterbi decoding is a good forward error correction technique suitable for channels affected by noise degradation. Fangled Viterbi decoders are variants of Viterbi decoder (VD) which decodes quicker and takes less memory with no error detection capability. Modified fangled takes it a step further by gaining one bit error correction and detection capability at the cost of doubling the computational complexity and processing time. A new efficient fangled Viterbi algorithm is proposed in this paper with less complexity and processing time along with 2 bit error correction capabilities. For 1 bit error correction for 14 bit input data, when compared with Modified fangled Viterbi decoder, computational complexity has come down by 36-43% and processing delay was halved. For a 2 bit error correction, when compared with Modified fangled decoder computational complexity decreased by 2236%.

Generalized MIMO transmit preprocessing using pilot symbol assisted rateless codes

In this paper, we propose a generalized multipleinput multiple-output (MIMO) transmit preprocessing system, where both the channel coding and the linear MIMO transmit precoding components exploit the knowledge of the channel. This was achieved by exploiting the inherently flexible nature of a specific family of rateless codes that are capable of modifying their code-rate as well as their degree distribution based on the channel state information (CSI), in an attempt to adapt to the time-varying nature of the channel. Moreover, we also propose a novel technique, hereby referred to as pilot symbol assisted rateless (PSAR) coding, where a predetermined fraction of binary pilot symbols is interspersed with the channel-coded bits at the channel coding stage, instead of multiplexing the pilots with the data symbols at the modulation stage, as in classic pilot symbol assisted modulation (PSAM). We will subsequently demonstrate that the PSAR code-aided transmit preprocessing scheme succeeds in gleaning more beneficial knowledge from the inserted pilots, because the pilot bits are not only useful for estimating the channel at the receiver, but they are also beneficial in terms of significantly reducing the computational complexity of the rateless channel decoder. Our results suggest that more than a 30% reduction in the decoder's computational complexity can be attained by the proposed system, when compared to a corresponding benchmarker scheme having the same pilot overhead but using the PSAM technique.

Flexible distribution of complexity by hybrid predictive-distributed video coding

There is currently limited flexibility for distributing complexity in a video coding system. While rate-distortion-complexity (RDC) optimization techniques have been proposed for conventional predictive video coding with encoder-side motion estimation, they fail to offer true flexible distribution of complexity between encoder and decoder since the encoder is assumed to have always more computational resources available than the decoder. On the other hand, distributed video coding solutions with decoder-side motion estimation have been proposed, but hardly any RDC optimized systems have been developed. To offer more flexibility for video applications involving multi-tasking or battery-constrained devices, in this paper, we propose a codec combining predictive video coding concepts and techniques from distributed video coding and show the flexibility of this method in distributing complexity. We propose several modes to code frames, and provide complexity analysis illustrating encoder and decoder computational complexity for each mode. Rate distortion results for each mode indicate that the coding efficiency is similar. We describe a method to choose which mode to use for coding each inter frame, taking into account encoder and decoder complexity constraints, and illustrate how complexity is distributed more flexibly.

A Hybrid ARQ Scheme Based on Rate-Compatible Low-Density Parity-Check Codes by Shortening and Extending

Incremental Redundancy Hybrid ARQ (IR-HARQ) based on rate-compatible punctured low-density parity-check (LDPC) codes can achieve high throughput over a wide range of SNRs. One drawback of such IR-HARQ schemes is high computational complexity of decoding for early transmission at high rates. In order to overcome this problem, a HARQ scheme based on rate-compatible LDPC codes by shortening and extending is presented in this paper. In the HARQ scheme, a high-rate mother code is transmitted at first, and parity-bits of a shortened code are transmitted for early retransmission requests. With a low-complexity decoder of the high-rate mother code, this shortened-code approach would result in low computational complexity of decoding, but it causes smaller length and larger number of shortened codes to be decoded as retransmission repeats. To prevent the resultant degradation of performance and complexity, extending is efficiently applied to the shortened codes after predetermined retransmission-times. A multi-edge type code-design is employed to construct irregular LDPC codes that meet the requirement of the HARQ scheme. Simulation results show that the HARQ scheme can achieve lower computational complexity of decoding than a conventional IR-HARQ scheme with good throughput over a wide range of SNRs.