Efficient universal lossless data compression algorithms based on agreedy sequential grammar transform. I. Without context models

A grammar transform is a transformation that converts any data sequence to be compressed into a grammar from which the original data sequence can be fully reconstructed. In a grammar-based code, a data sequence is first converted into a grammar by a grammar transform and then losslessly encoded. In this paper, a greedy grammar transform is first presented; this grammar transform constructs sequentially a sequence of irreducible grammars from which the original data sequence can be recovered incrementally. Based on this grammar transform, three universal lossless data compression algorithms, a sequential algorithm, an improved sequential algorithm, and a hierarchical algorithm, are then developed. These algorithms combine the power of arithmetic coding with that of string matching. It is shown that these algorithms are all universal in the sense that they can achieve asymptotically the entropy rate of any stationary, ergodic source. Moreover, it is proved that their worst case redundancies among all individual sequences of length n are upper-bounded by c log log n/log n, where c is a constant. Simulation results show that the proposed algorithms outperform the Unix Compress and Gzip algorithms, which are based on LZ78 and LZ77, respectively     

一种用于文本压缩的信源容错译码算法

LZ算法在文本压缩领域应用广泛。LZ译码以先前接收码字的译码结果形成字典,后续译码依赖于先前的重构数据,一旦压缩码字出现误码将会引起严重的误码扩散。分析了主流的LZ77算法编译码原理,讨论了输入误码对译码字典和解压数据的影响,研究了误码传播问题。在此基础上提出一种用于文本压缩数据的容错译码算法,指出容错处理对抑制误码传播及保证LZ77解压数据的完整性具有重要意义。     

Better OPM/L Text Compression

An OPM/L data compression scheme suggested by Ziv and Lempel, LZ77, is applied to text compression. A slightly modified version suggested by Storer and Szymanski, LZSS, is found to achieve compression ratios as good as most existing schemes for a wide range of texts. LZSS decoding is very fast, and comparatively little memory is required for encoding and decoding. Although the time complexity of LZ77 and LZSS encoding isO(M)for a text ofMcharacters, straightforward implementations are very slow. The time consuming step of these algorithms is a search for the longest string match. Here a binary search tree is used to find the longest string match, and experiments show that this results in a dramatic increase in encoding speed. The binary tree algorithm can be used to speed up other OPM/L schemes, and other applications where a longest string match is required. Although the LZSS scheme imposes a limit on the length of a match, the binary tree algorithm will work without any limit.     

The smallest grammar problem

This paper addresses the smallest grammar problem: What is the smallest context-free grammar that generates exactly one given string /spl sigma/? This is a natural question about a fundamental object connected to many fields such as data compression, Kolmogorov complexity, pattern identification, and addition chains. Due to the problem's inherent complexity, our objective is to find an approximation algorithm which finds a small grammar for the input string. We focus attention on the approximation ratio of the algorithm (and implicitly, the worst case behavior) to establish provable performance guarantees and to address shortcomings in the classical measure of redundancy in the literature. Our first results are concern the hardness of approximating the smallest grammar problem. Most notably, we show that every efficient algorithm for the smallest grammar problem has approximation ratio at least 8569/8568 unless P=NP. We then bound approximation ratios for several of the best known grammar-based compression algorithms, including LZ78, B ISECTION, SEQUENTIAL, LONGEST MATCH, GREEDY, and RE-PAIR. Among these, the best upper bound we show is O(n/sup 1/2/). We finish by presenting two novel algorithms with exponentially better ratios of O(log/sup 3/n) and O(log(n/m/sup */)), where m/sup */ is the size of the smallest grammar for that input. The latter algorithm highlights a connection between grammar-based compression and LZ77.     

On the average redundancy rate of the Lempel-Ziv code

In this paper, we settle a long-standing open problem concerning the average redundancy r_n of the Lempel-Ziv'78 (LZ78) code. We prove that for a memoryless source the average redundancy rate attains asymptotically Er_n=(A+δ(n))/log n+ O(log log n/log² n), where A is an explicitly given constant that depends on source characteristics, and δ(x) is a fluctuating function with a small amplitude. We also derive the leading term for the kth moment of the number of phrases. We conclude by conjecturing a precise formula on the expected redundancy for a Markovian source. The main result of this paper is a consequence of the second-order properties of the Lempel-Ziv algorithm obtained by Jacquet and Szpankowski (1995). These findings have been established by analytical techniques of the precise analysis of algorithms. We give a brief survey of these results since they are interesting in their own right, and shed some light on the probabilistic behavior of pattern matching based data compression     

Improving of entropy adaptive on-line compression

Since energy efficiency, high bandwidth, and low transmission delay are challenging issues in mobile networks, due to resource constraints, there is a great importance in designing of new communication methods. In particular, lossless data compression may provide high performance under constrained resources. In this paper we present a novel on-line and entropy adaptive compression scheme for streaming unbounded length inputs. The scheme extends the window dictionary Lempel–Ziv compression and is adaptive and tailored to compress on-line non entropy stationary inputs. Specifically, the window dictionary size is changed in an adaptive manner to fit the current best compression rate for the input. On-line entropy adaptive compression scheme (EAC), introduced and analyzed in this paper, examines all possible sliding window sizes over the next input portion to choose the optimal window size for this portion; a size that implies the best compression ratio. The size found is then used in the actual compression of this portion. We suggest an adaptive encoding scheme, which optimizes the parameters block by block, and base the compression performance on the optimality proof of LZ77 when applied to blocks (Ziv in IEEE Trans Inf Theory 55(5):1941–1944, 2009). This adaptivity can be useful for many communication tasks. In particular, providing efficient utilization of energy consuming wireless devices by data compression. Due to the dynamic and non-uniform structure of multimedia data, adaptive approaches for data processing are of special interest. The EAC scheme was tested on different types of files (docx, ppt, jpeg, xls) and over synthesized files that were generated as segments of homogeneous Markov Chains. Our experiments demonstrate that the EAC scheme typically provides a higher compression ratio than LZ77 does, when examined in the scope of on-line per-block compression of transmitted (or compressed) files. We propose techniques intended to control the adaptive on-line compression process by estimating relative entropy between two sequential blocks of data. This approach may enhance performance of the mobile networks.     

The sliding-window Lempel-Ziv algorithm is asymptotically optimal

The sliding-window version of the Lempel-Ziv data-compression algorithm (sometimes called LZ '77) has been thrust into prominence recently. A version of this algorithm is used in the highly successful “Stacker” program for personal computers. If is also incorporated into Microsoft's new MS-DOS-6. Although other versions of the Lempel-Ziv algorithm are known to he optimal in the sense that they compress a data source to its entropy, optimality in this sense has never been demonstrated for this version. In this self-contained paper, we will describe the algorithm, and show that as the “window size,“ a quantity which is related to the memory and complexity of the procedure, goes to infinity, the compression rate approaches the source entropy. The proof is surprisingly general, applying to all finite-alphabet stationary ergodic sources     

不同压缩算法性能的研究

移动通信网络中，建立一次多媒体会话通常需要数十秒钟的时间。通过对信令消息的压缩可以有效地减少所需时延，改善服务质量。文章先后使用了LZ77、LZW和Deflate压缩算法对因特网协议多媒体子系统中的会话发起协议信令消息的压缩进行了研究。仿真结果显示：Deflate算法的压缩性能最好，不使用辞典时压缩率可以达到30％，使用辞典时压缩率可以达到50％以上；接着是LZW算法，而LZ77算法的压缩性能最差。     

自适应字典压缩算法中的误码传播分析

在分析LZ77算法编译码原理的基础上,讨论了输入误码对译码字典和解压数据的影响,研究了误码传播问题。指出这些工作为消除误码传播、保证数据完整性具有重要意义。     

水声通信数据无损压缩方法的对比研究

为了选择适合水声通信数据无损压缩的算法,对哈夫曼压缩算法和LZ77压缩算法进行了对比研究。通过C语言编程实现两种算法的压缩,并利用水声通信数据获得压缩结果。对两种算法的压缩率和压缩效率对比分析之后,得出结论：对于水声信号,使用哈夫曼算法将获得更好的压缩率和压缩速率。尤其是哈夫曼算法的压缩速率远远优于LZ77算法。     

The Universal LZ77 Compression Algorithm Is Essentially Optimal for Individual Finite-Length $N$-Blocks

Consider the case where consecutive blocks of N letters of a semi-infinite individual sequence X over a finite alphabet are being compressed into binary sequences by some one-to-one mapping. No a priori information about X is available at the encoder, which must therefore adopt a universal data-compression algorithm. It is known that there exist a number of asymptotically optimal universal data compression algorithms (e.g., the Lempel-Ziv (LZ) algorithm, context tree algorithm and an adaptive Hufmann algorithm) such that when successively applied to N-blocks then, the best error-free compression for the particular individual sequence X is achieved as N tends to infinity. The best possible compression that may be achieved by any universal data compression algorithm for finite N-blocks is discussed. Essential optimality for the compression of finite-length sequences is defined. It is shown that the LZ77 universal compression of N-blocks is essentially optimal for finite N-blocks. Previously, it has been demonstrated that a universal context tree compression of N blocks is essentially optimal as well.     

On Certain Pathwise Properties of the Sliding-Window Lempel–Ziv Algorithm

We derive several almost-sure results related to the sliding-window Lempel-Ziv (SWLZ) algorithm. A principal result is a path-wise lower bound to the redundancy equal to 1/2hlog₂log ₂n_w/log₂n_w in the main term, where n_w is the sliding window size. This bound is off by a factor of two from the main term in the lower bound of A. J. Wyner and the work of Yang and Kieffer, which hold in the expected sense for the fixed-database Lempel-Ziv algorithm (FDLZ). Another aspect of the present work studies the asymptotic behavior of the ratio of the number of phrases to the length of the parsed string for any finite sliding window size; in here we exploit the theory of asymptotic mean stationary processes of Gray and Kieffer and some results of Kieffer and Rahe. In all cases it is assumed that the source is stationary and that in the most restrictive case it is an irreducible and aperiodic Markov chain; some of the results hold for sources that have exponential rates for entropy and more generally for the ergodic setting     

远程控制中视频信号压缩问题的解决方案

描述JPEG和LZ77压缩算法原理．并通过实际软件仿真进行比较，认证了DSP(Digital Signal Processor)适合于JPEG图像压缩算法。然后通过计算机和DSP的JPEG压缩速度的比较，提出了远程控制中视频信号压缩问题的解决方案。     

Is layering, harmful? [remote procedure call]

Remote procedure call (RPC) mechanisms over the US Department of Defense transmission control protocol. (TCP) can produce behavior analogous to the silly window syndrome because of a mismatched interface between the socket and the TCP modules. The detection and diagnosis of the problem are addressed. Some pointers to a design approach that could avoid the problems of mismatched communication layers are provided     

Simplistic universal coding

A conceptually simple coding method may be described as follows. The source sequence is parsed into fixed-length blocks and a list of these blocks is placed in a dictionary. In the lossless case, the dictionary is transmitted and each successive block is encoded by giving its dictionary location. In the lossy case, the smallest collection of blocks such that every member of the dictionary is within distortion δ of the collection is determined, this codebook is transmitted, and each successive block is encoded by giving the location of a member of the code within δ of it. We show that by optimizing on the block length, this method is universal, that is, for any ergodic process it achieves entropy in the limit in the lossless case and the rate-distortion function R(δ) in the lossy case     

一种基于字节型多变长码的串匹配的Alpha图像编码算法

根据 Alpha 图像的特征和串匹配算法的编码参数统计特性,提出了一种基于字节型多变长码的串匹配的 Alpha 图像编码算法。该算法首先对多个串匹配编码参数采用字节型多变长码方案进行联合优化编码,然后采用邻近偏移量优先的分段映射方案对偏移量参数进行编码,最后对匹配串长度参数采用分段编码方案进行编码。实验结果表明,本文提出的算法与LZ4HC、zlib、PNG、HEVC（x265）相比,都具有超低复杂度兼高编码效率的优势。     

Efficient Implementation Methodology of Fast FIR Filtering Algorithms on DSP

A class of Finite Impulse Response (FIR) filtering algorithms based either on short Fast Fourier Transforms (FFT) or on short length FIR filtering algorithms was recently proposed. Besides the significant reduction of the arithmetic complexity, these algorithms present some characteristics which make them useful in many applications, namely a small delay processing (independent on the FIR filter length) as well as a multiply-add based computational structure. These algorithms are presented in a unified framework, thus allowing an easy combination of any of them. However, a remaining difficulty concerns the implementation of the fast algorithms on Digital Signal Processors (DSP), given the DSP finite resources (number of pointers, registers and memory), while keeping as much as possible the improvement brought by the reduction of the arithmetic complexity. This paper provides an efficient implementation methodology, by organizing the algorithm in such a way that the memory data access is optimized on a DSP. As a result, our implementation requires a constant number of pointers whatever the algorithm combination. This knowledge is used in a DSP code generator which is able to select the appropriate algorithm meeting the application constraints, as well as to generate automatically an optimized assembly code, using macro-instructions available in a DSP-dependent library. An improvement of more than 50% in terms of throughput (number of machine cycles per point) compared to the implementation of the direct convolution is generally achieved.     

Design of sequence set with group-wise zero correlation window

Zero correlation window (ZCW) or zero correlation zone (ZCZ) sequence can be used in quasi-synchronous code division multiple access (QS-CDMA) system to eliminate multiple access and multipath interferences. However, as the length of ZCW or ZCZ increases, fewer sequences are available. Recently, a new concept, sequence set with group-wise zero correlation window is introduced, which can increase the number of available sequences for a QS-CDMA system. In this article, a new method for generating sequence set with group-wise zero correlation window is presented. This method is based on a Hadamard matrix of size N×N and a pair of Hadamard matrices of size M×M. Compared with previous methods, the proposed sequence set has a group-wise zero correlation window for both periodic and aperiodic cross-correlation functions.     

Textural feature based face recognition for single training images

A novel face recognition algorithm using single training face image is proposed. The algorithm is based on textural features extracted using the 2D log Gabor wavelet. These features are encoded into a binary pattern to form a face template which is used for matching. Experimental results show that on the colour FERET database the accuracy of the proposed algorithm is higher than the local feature analysis (LFA) and correlation filter (CF) based face recognition algorithms even when the number of training images is reduced to one. In comparison with recent single training image based face recognition algorithms, the proposed 2D log Gabor wavelet based algorithm shows an improvement of more than 3% in accuracy.     

Parallel routing algorithms in Benes-Clos networks

A new parallel algorithm for route assignments in Benes-Clos (1962, 1953) networks is studied. Most known sequential route assignment algorithms, such as the looping algorithm, are designed for circuit switching systems where the switching configuration can be rearranged at relatively low speed. In packet switching systems, switch fabrics must be able to provide internally conflict-free paths simultaneously, and accommodate packets requesting connections in real time as they arrive at the inputs. In this paper, we develop a parallel routing algorithm for Benes networks by solving a set of Boolean equations which are derived from the connection requests and the symmetric structure of the networks. Our approach can handle partial permutations easily. The time complexity of our algorithm is O(log/sup 2/ N), where N is the network size. We also extend the algorithm and show that it can be applied to the Clos networks if the number of central modules is M=2/sup m/, where m is a positive integer. The time complexity is O(log N/spl times/log M) in this case.