Asymmetric Numeral Systems Research Articles

Fast and Efficient Entropy Coding Architectures for Massive Data Compression

The compression of data is fundamental to alleviating the costs of transmitting and storing massive datasets employed in myriad fields of our society. Most compression systems employ an entropy coder in their coding pipeline to remove the redundancy of coded symbols. The entropy-coding stage needs to be efficient, to yield high compression ratios, and fast, to process large amounts of data rapidly. Despite their widespread use, entropy coders are commonly assessed for some particular scenario or coding system. This work provides a general framework to assess and optimize different entropy coders. First, the paper describes three main families of entropy coders, namely those based on variable-to-variable length codes (V2VLC), arithmetic coding (AC), and tabled asymmetric numeral systems (tANS). Then, a low-complexity architecture for the most representative coder(s) of each family is presented—more precisely, a general version of V2VLC, the MQ, M, and a fixed-length version of AC and two different implementations of tANS. These coders are evaluated under different coding conditions in terms of compression efficiency and computational throughput. The results obtained suggest that V2VLC and tANS achieve the highest compression ratios for most coding rates and that the AC coder that uses fixed-length codewords attains the highest throughput. The experimental evaluation discloses the advantages and shortcomings of each entropy-coding scheme, providing insights that may help to select this stage in forthcoming compression systems.

High efficiency lossless image recompression algorithm with asymmetric numeral systems for real-time mobile application

High efficiency lossless image recompression algorithm with asymmetric numeral systems for real-time mobile application

The Compression Optimality of Asymmetric Numeral Systems.

Source coding has a rich and long history. However, a recent explosion of multimedia Internet applications (such as teleconferencing and video streaming, for instance) renews interest in fast compression that also squeezes out as much redundancy as possible. In 2009 Jarek Duda invented his asymmetric numeral system (ANS). Apart from having a beautiful mathematical structure, it is very efficient and offers compression with a very low coding redundancy. ANS works well for any symbol source statistics, and it has become a preferred compression algorithm in the IT industry. However, designing an ANS instance requires a random selection of its symbol spread function. Consequently, each ANS instance offers compression with a slightly different compression ratio. The paper investigates the compression optimality of ANS. It shows that ANS is optimal for any symbol sources whose probability distribution is described by natural powers of 1/2. We use Markov chains to calculate ANS state probabilities. This allows us to precisely determine the ANS compression rate. We present two algorithms for finding ANS instances with a high compression ratio. The first explores state probability approximations in order to choose ANS instances with better compression ratios. The second algorithm is a probabilistic one. It finds ANS instances whose compression ratios can be made as close to the best ratio as required. This is done at the expense of the number θ of internal random "coin" tosses. The algorithm complexity is O(θL3), where L is the number of ANS states. The complexity can be reduced to O(θLlog2L) if we use a fast matrix inversion. If the algorithm is implemented on a quantum computer, its complexity becomes O(θ(log2L)3).

Lightweight compression with encryption based on asymmetric numeral systems

Data compression combined with effective encryption is a common requirement of data storage and transmission. Low cost of these operations is often a high priority in order to increase transmission speed and reduce power usage. This requirement is crucial for battery-powered devices with limited resources, such as autonomous remote sensors or implants. Well-known and popular encryption techniques are frequently too expensive. This problem is on the increase as machine-to-machine communication and the Internet of Things are becoming a reality. Therefore, there is growing demand for finding trade-offs between security, cost and performance in lightweight cryptography. This article discusses Asymmetric Numeral Systems -- an innovative approach to entropy coding which can be used for compression with encryption. It provides compression ratio comparable with arithmetic coding at similar speed as Huffman coding, hence, this coding is starting to replace them in new compressors. Additionally, by perturbing its coding tables, the Asymmetric Numeral System makes it possible to simultaneously encrypt the encoded message at nearly no additional cost. The article introduces this approach and analyzes its security level. The basic application is reducing the number of rounds of some cipher used on ANS-compressed data, or completely removing additional encryption layer if reaching a satisfactory protection level.

REDUCTION OF PAPR USING ASYMMETRIC NUMERAL SYSTEM QC-LDPC WITH HUFFMAN AND ARITHMETIC CODING FOR F-OFDMA SYSTEM

As modern wireless communication systems move towards 5G implementation, the system must provide sophisticated and ubiquitous service and flexibility. Therefore, Filtered Orthogonal Frequency Division Multiple Access (F-OFDMA) is one of the most suitable modulation techniques used in 5G systems to achieve efficient and reliable wireless communication. Other than that, F-OFDMA also has good quality rather than OFDM since it provides a better result of high side lobes and enlarges the scale of the spectrum analyzer. However, one of the significant problems in the F-OFDMA system is the high peak-to-average power ratio (PAPR), affecting the system's overall performance and causing high transmit power at the transmitter. In this paper, combination of Arithmetic Coding (AC) and Huffman coding (HC) with Asymmetric Numeral Systems (ANS) provide better performance for PAPR as well as bit error rate (BER) in F-OFDMA. Both AC and HC are proposed to combine with ANS and Quasi-Cyclic Low-Density Parity Check (QC-LDPC) since it provides a good result to defeat the high PAPR. BER and PAPR performance were compared for the AC and HC with ANS QC-LDPC. Based on the results, ANS-AC-QCLDPC proved as the best joint method has 35.25% improvement for PAPR while BER has 89.87%. This research also justified that ANS with Arithmetic-QCLDPC and Huffman-QCLDPC give better BER results as well.

An FPGA-Based LOCO-ANS Implementation for Lossless and Near-Lossless Image Compression Using High-Level Synthesis

In this work, we present and evaluate a hardware architecture for the LOCO-ANS (Low Complexity Lossless Compression with Asymmetric Numeral Systems) lossless and near-lossless image compressor, which is based on JPEG-LS standard. The design is implemented in two FPGA generations, evaluating its performance for different codec configurations. The tests show that the design is capable of up to 40.5 MPixels/s and 124 MPixels/s per lane for Zynq 7020 and UltraScale+ FPGAs, respectively. Compared to the single thread LOCO-ANS software implementation running in a 1.2 GHz Raspberry Pi 3B, each hardware lane achieves 6.5 times higher throughput, even when implemented in an older and cost-optimized chip like the Zynq 7020. Results are also presented for a lossless only version, which achieves a lower footprint and approximately 50% higher performance than the version that supports both lossless and near-lossless. Interestingly, these great results were obtained applying High-Level Synthesis, describing the coder with C++ code, which tends to establish a trade-off between design time and quality of results. These results show that the algorithm is very suitable for hardware implementation. Moreover, the implemented system is faster and achieves higher compression than the best previously available near-lossless JPEG-LS hardware implementation.

LOCO-ANS: An Optimization of JPEG-LS Using an Efficient and Low-Complexity Coder Based on ANS

Near-lossless compression is a generalization of lossless compression, where the codec user is able to set the maximum absolute difference (the error tolerance) between the values of an original pixel and the decoded one. This enables higher compression ratios, while still allowing the control of the bounds of the quantization errors in the space domain. This feature makes them attractive for applications where a high degree of certainty is required. The JPEG-LS lossless and near-lossless image compression standard combines a good compression ratio with a low computational complexity, which makes it very suitable for scenarios with strong restrictions, common in embedded systems. However, our analysis shows great coding efficiency improvement potential, especially for lower entropy distributions, more common in near-lossless. In this work, we propose enhancements to the JPEG-LS standard, aimed at improving its coding efficiency at a low computational overhead, particularly for hardware implementations. The main contribution is a low complexity and efficient coder, based on Tabled Asymmetric Numeral Systems (tANS), well suited for a wide range of entropy sources and with simple hardware implementation. This coder enables further optimizations, resulting in great compression ratio improvements. When targeting photographic images, the proposed system is capable of achieving, in mean, 1.6%, 6%, and 37.6% better compression for error tolerances of 0, 1, and 10, respectively. Additional improvements are achieved increasing the context size and image tiling, obtaining 2.3% lower bpp for lossless compression. Our results also show that our proposal compares favorably against state-of-the-art codecs like JPEG-XL and WebP, particularly in near-lossless, where it achieves higher compression ratios with a faster coding speed.

A simplified variant of tabled asymmetric numeral systems with a smaller look-up table

Data storage is an indispensable part of data management system. Asymmetric numeral systems (ANS) is a widely used compression algorithm. A number of implementations, such as range asymmetric numeral systems (rANS) and tabled asymmetric numeral systems (tANS), were proposed. However, rANS requires some costly arithmetic operations (integer additions, multiplications and divisions), and tANS requires large space to store the entire behavior in a look-up table. When the integer addition is allowed, this paper proposes a variant of tANS, that requires much smaller look-up table than the conventional tANS. In addition, a decoding algorithm to decode multiple symbols at once is proposed. The simulation shows that with a slight loss of compression ratio (approximately $$0.5\%$$ lower), the proposed method has up to a $$25\%$$ ( $$60\%$$ ) better throughput than rANS in encoding (decoding).

Large-Alphabet Semi-Static Entropy Coding Via Asymmetric Numeral Systems

An entropy coder takes as input a sequence of symbol identifiers over some specified alphabet and represents that sequence as a bitstring using as few bits as possible, typically assuming that the elements of the sequence are independent of each other. Previous entropy coding methods include the well-known Huffman and arithmetic approaches. Here we examine the newer asymmetric numeral systems (ANS) technique for entropy coding and develop mechanisms that allow it to be efficiently used when the size of the source alphabet is large—thousands or millions of symbols. In particular, we examine different ways in which probability distributions over large alphabets can be approximated and in doing so infer techniques that allow the ANS mechanism to be extended to support large-alphabet entropy coding. As well as providing a full description of ANS, we also present detailed experiments using several different types of input, including data streams arising as typical output from the modeling stages of text compression software, and compare theproposed ANS variants with Huffman and arithmetic coding baselines, measuring both compression effectiveness and also encoding and decoding throughput. We demonstrate that in applications in which semi-static compression is appropriate, ANS-based coders can provide an excellent balance between compression effectiveness and speed, even when the alphabet is large.

Low-complexity lossless multichannel ECG compression based on selective linear prediction

In this paper we present low-complexity method for multichannel lossless compression, dedicated for portable ECG acquisition systems. Each channel is selectively decorrelated using two linear predictors, separately for the heart beats and the background signal. Next, cross-channel correlations are used to determine pairs of strongly dependent channels, which allows for further decorrelation of signals using cross-channel predictors. Prediction is therefore obtained at small computational cost, using a simple QRS detector and three short linear predictors per channel, updated periodically using fast Levinson-Durbin recursion. Finally, the prediction error and the estimate of its variance is used in entropy encoding with highly effective method of asymmetric numeral systems. The average compression ratio depends on the similarity between channels and varies from 2.92 (MIT-BIH ADB, low similarity) to 3.43 (INCART, high similarity).

Huffman Coding

Huffman’s algorithm for computing minimum-redundancy prefix-free codes has almost legendary status in the computing disciplines. Its elegant blend of simplicity and applicability has made it a favorite example in algorithms courses, and as a result it is perhaps one of the most commonly implemented algorithmic techniques. This article presents a tutorial on Huffman coding and surveys some of the developments that have flowed as a consequence of Huffman’s original discovery, including details of code calculation and of encoding and decoding operations. We also survey related mechanisms, covering both arithmetic coding and the recently developed asymmetric numeral systems approach and briefly discuss other Huffman-coding variants, including length-limited codes.

An Architecture for Asymmetric Numeral Systems Entropy Decoder - A Comparison with a Canonical Huffman Decoder

This paper proposes two decoder hardware architectures for the tabled asymmetric numeral systems (tANS) compression algorithm, a software implementation of which is used by Apple and Facebook due to its efficiency. To the best of our knowledge, hardware architectures for the highly efficient tANs algorithm are investigated by the authors so far uniquely. The tANS decoder hardware architectures have been compared to a novel Huffman decoder hardware architecture because the Huffman coding is known as one of the fastest coding techniques in hardware and software. For the proposed architectures, the decoding throughput is highly dependent on the compression ratio of data. Experimental results show that the proposed tANS architecture outperforms the tANS software decoder and can achieve the throughput up to 200MB/s using current FPGA technology. Compared to canonical Huffman decoder the proposed hardware architecture provides up to four times higher decoding throughput.