Abstract:
A technique is presented for compressing data which leverages the frequency of an escape symbol for better compression. The prefix of a data string is evaluated and the probability of all characters that might succeed it is predicted in tabular form. Symbols are designated “Hit” or “Miss” based upon whether they are in the table. A binary tree is generated by partitioning nodes into Zero and One groups based on a single bit value. A partition bit is chosen to maximize the difference of probability sums of Hit symbols in Zero and One groups, with exceptions for partitions having non Hit symbols in one of the groups. A probability value is assigned to each branch, based on the probabilities of Hit and Miss symbols. Encoding a symbol is facilitated by encoding the branch probabilities on the shortest path from the root to the leaf node containing the symbol using arithmetic encoding.

Description:
II. RELATED ART  
         [0001]    It is highly desirable to compress data so that it can be efficiently stored and transmitted. Valuable bandwidth can be preserved and communication channels can be more efficiently used if the size of the data is reduced. Similarly, less memory is required to store compressed data than non-compressed data. Various different techniques such as run length encoding (for example, Ziv-Lempel and PK Zip), Huffman compression, and arithmetic coding can be used to compress data in such a way that data is not lost. These lossless techniques can be performed in conjunction with other algorithms that enhance compression, such as the Burrows-Wheeler transform.  
           [0002]    A simple variant of run length encoding involves identifying one or more strings of data that are frequently repeated, such as the word “the”. Such frequently repeated data strings can be encoded using a coding element that is substantially shorter than the string itself. This technique and variants thereof can achieve up to approximately 4:1 compression of English text. More complex variants of run length encoding are also in common use. A major drawback to run length encoding is that the strings of data that are frequently repeated are not always known a priori, thus requiring the use of a pre-determined set of codes for a set of predetermined repetitive symbols. It may not be possible to achieve the desired degree of compression if the repetitive strings in the data do not match those included in the pre-determined set.  
           [0003]    Huffman coding or variants thereof, is used in a variety of instances, ranging from Morse code, to the UNIX pack/unpack and compress/uncompress commands. Huffman coding and variants of Huffman coding involve determining the relative frequency of characters and assigning a code based upon that particular frequency. Characters that recur frequently have shorter codes than characters that occur less frequently. Binary tree structures are generated, preferably starting at the bottom with the longest codes, and working to the top and ending with the shortest codes. Although preferably built from the bottom up, these trees are actually read from the top down, as the decoder takes a bit-encoded message and traces the branches of the tree downward. In this way, the most frequently encountered characters are encountered first. One of the drawbacks to Huffman coding is that the probabilities assigned to characters are not known a priori. Generally, the Huffman binary tree is generated using pre-established frequencies that may or may not apply to a particular data set.  
           [0004]    Arithmetic coding is also used in a variety of circumstances. Generally, compression ratios achieved using arithmetic coding are higher than those achieved using Huffman coding when the probabilities of data elements are more arbitrary. Like Huffman coding, arithmetic encoding is a lossless technique based upon the probability of a data element. However, unlike Huffman coding, arithmetic coding produces a single symbol rather than several separate code words. Data is encoded as a real number in an interval from one to zero (as opposed to a whole number). Unfortunately, arithmetic coding presents a variety of drawbacks. First, arithmetic coding is generally much slower than other techniques. This is especially serious when arithmetic encoding is used in conjunction with high-order predictive coding methods. Second, because arithmetic coding more faithfully reflects the probability distribution used in an encoding process, inaccurate or incorrect modeling of the symbol probabilities may lead to poorer performances.  
           [0005]    Adaptive statistics provides a technique for dealing with some of the drawbacks involving prior knowledge of a symbol set. In general, adaptive encoding algorithms provide a way to encode symbols that are not present in a table of symbols or a table of prefixes. If an unknown symbol is detected, an escape code (ESC value) is issued and entered into the coded stream. The encoder continues the encoding process with a lower order prefix, adding additional data to the encoded bit stream. The lowest order prediction table (often a order 0 table) must contain all possible symbols so that every possible symbol can be found in it. The ESC code must be encoded using a probability. However, because of the unpredictable nature of new symbols, the probability of the ESC code cannot be accurately estimated from preceding data. Often, the probability of the ESC value for a given prefix is empirically determined, leading to non-optimal efficiency. Thus, introduction of an ESC code in adaptive encoding algorithms raises two problems. Firstly, the ESC code only gives limited information about the new symbol; the new symbol still has to be encoded using a lower order of prefix prediction table. The second problem is that the probability of the ESC code can not be accurately modeled.  
           [0006]    Accordingly, it would be advantageous to provide a technique for lossless compression that does not suffer from the drawbacks of the prior art.  
         SUMMARY OF THE INVENTION  
         [0007]    The invention provides a technique for efficiently compressing data by reducing the effect of inaccurate modeling of the escape code (ESC) used in adaptive encoding algorithms so as to achieve a high degree of lossless compression.  
           [0008]    In a first aspect of the invention, the prefix of a data string is evaluated and the probability of all characters that might succeed that prefix is predicted. A table comprised of all these probabilities is generated from the preceding data that has been encoded. In a preferred embodiment, the prefix may be comprised of one or two elements. Although the size of the prefix may be highly variable, the prefix is preferably an order 3 prefix or smaller so as to limit the number of values that will be recorded.  
           [0009]    In a second aspect of the invention, a binary tree is constructed. Unlike binary trees used in Huffman coding, the tree is generated so as to be as unbalanced as possible for the symbols found in the prediction table. For an M-bit representation of the symbols, a binary tree may have up to M layers with each layer corresponding to a bit-based partition of the symbols.  
           [0010]    In a preferred embodiment, a binary tree starts from a root node which contains a full set of all possible symbols. The root splits into two branches, each leading to a node. Each node contains a group of symbols which have a common value at a particular bit position. The branching is based on the value of a single bit in a binary representation of the symbols. If a symbol has a 0 value at this bit, then the symbol is put into a group called “Zero group”. If a symbol has a value of 1 at this bit, then the symbols is put into a group called “One group”. For example, if b 1  bit is used to do the partition in a 3-bit representation b 2 b 1 b 0  of the symbols, then all symbols (like 101, 000) of the form X0X are put into a Zero group, and all symbols (like 110, 011) of the form X1X are put into a One group, where X can be either 0 or 1. The choice of the particular bit position for partitioning a node follows an unusual rule to optimize the coding efficiency. A binary tree ends at leaves, each of which is a symbol.  
           [0011]    In a third aspect of the invention, it is possible to efficiently evaluate and encode symbols that do not appear in the probability table and are particularly difficult to efficiently compress using conventional compression techniques. For example, in Huffman coding, the frequency of these unknown symbols or escape values may be very high, thus requiring a short code (and thereby lengthening the code used for other known symbols). In a preferred embodiment, a symbol is encoded traversing the path from the root to the symbol in the associated binary tree. Unlike conventional approaches which encode a symbol in a single step, in the preferred embodiment, a symbol is encoded in several steps with each step corresponding to a layer in the binary tree. Effectively, a symbol is encoded bit by bit. This bitwise decomposition brings in two advantages. First, bitwise decomposition delays the use of the ESC value to a later time when there is less uncertainty about what the coming symbol will be. Second, it also traces the ESC value to the particular symbol that is escaped, eliminating the need of encoding the symbol again with a lower order prefix. The path encoded will lead to full discovery of the symbol as the binary tree must eventually end to a symbol along any path. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0012]    [0012]FIG. 1 is a block diagram of an encoding system using prefix prediction.  
         [0013]    [0013]FIGS. 2A and 2B are a block diagram of tables showing the probability of data elements in a sample prefix string.  
         [0014]    [0014]FIG. 3 is a data tree showing the distribution of probabilities in a sample prefix string.  
         [0015]    [0015]FIG. 4 is a flow diagram showing a method of data compression using prefix prediction encoding. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0016]    In the following description, a preferred embodiment of the invention is described with regard to preferred process steps and data structures. Embodiments of the invention can be implemented using general purpose processors or special purpose processors operating under program control, or other circuits, adapted to particular process steps and data structures described herein. Implementation of the process steps and data structures described herein would not require undue experimentation or further investigation.  
       System Elements  
       [0017]    [0017]FIG. 1 is a block diagram of an encoding system with prefix prediction.  
         [0018]    An encoding system using prefix prediction (indicated by general reference character  100 ) includes a computing device  110 . The computing device  110  comprises a central processing unit  115 , a memory  120 , and an input/output (I.O.) section  125  coupled to an operator interface  130 . The memory  120  can include any device for storing relatively large amounts of information, such as magnetic disks or tapes, optical devices, magneto-optical devices, or other types of mass storage. As used herein, the term “computing device” is intended in its broadest sense, and includes any device having a programmable processor or otherwise falling within the generalized Turing machine paradigm such as a personal computer, laptop or personal digital assistant.  
         [0019]    The memory  120  includes a computer program  140  comprising a set of instructions  145  (not shown) for the following four-stage procedure: (1) ordering a set of data, (2) performing a Burrows Wheeler transform, (3) performing predictive prefix encoding, and (4) performing arithmetic encoding. In a preferred embodiment, the memory  120  also includes a set of data  150  that will be manipulated using the computer program  140 .  
         [0020]    [0020]FIGS. 2A and 2B are a block diagram of tables showing the probability of data elements that may follow a sample prefix string. For the purposes of illustration, a set of 8 symbols, {A,B,C,D,E,F,G,H} are considered as the full set of symbols.  
         [0021]    Depending upon the nature of the data  150 , the system  100  may generate either an order 1 table  210 , an order 2 table  230 , or an order 0 table  250  or all of them. Examples of these tables are shown in this figure. These tables and the symbols therein are exemplary and in no way limiting. In other preferred embodiments, other order tables, such as order 3 tables may also be generated.  
         [0022]    The order 1 prediction table  210  includes a set of one or more prefix symbols  215 , a set of one or more possible symbols  220  that may follow each prefix symbol  215 , and a set of probability values  225 . The prefix symbols  215  are those symbols that are identified as being at the very beginning of a particular ordered string. The set of symbols  220  include both actual characters and an ESC  221 . The probability value  225  reflects the probability that a particular symbol  220  will follow the prefix symbol  215  in question. In an order 1 table  210 , each prefix symbol  215  is limited to one character in length.  
         [0023]    ESC is an escape value reflecting the collection of symbols not found in the current table. These “escaped” symbols are called Miss symbols. In contrast, those symbols found in the prediction table are called Hit symbols. In general, the probability of the ESC value is attributed to the collection of Miss symbols, but can hardly be accurately attributed to each particular symbol. However, ESC symbols in general will be further decomposed into symbols in the binary tree as discussed infra. In such cases, a shaped distribution of the ESC probability over all Miss symbols can be used. In table  210 , a uniform distribution of the ESC probability over Miss symbols is used.  
         [0024]    The order 2 prediction table  230  includes a set of one or more prefix symbols  235 , a set of one or more possible symbols  240  that may follow the prefix symbols  235 , and a probability value  245 . The prefix symbols  235  are those symbols that are identified as those at the very beginning of a particular string. The set of symbols  240  include both Hit Symbols and an ESC  241 . The ESC is an escape value reflecting the collection of Miss symbols in the current, order 2 table. The probability value  245  reflects the probability that a particular symbol  240  will follow the prefix symbol  235  in question. In an order 2 table  210 , each prefix symbol  215  is two characters in length.  
         [0025]    The order 0 prediction table  250  includes a null set of prefix symbols  255 , a set of one or more symbols  260  that may follow the prefix symbols  255  and a probability value  265 . Generally, the order  0  prediction table is applicable to the case when no prefix is used for encoding. The set of symbols  260  includes the full set of symbols and no ESC value, because the order 0 table contains all the possible symbols. The probability value  265  reflects the probability that a particular symbol  246  will follow the null prefix symbol  255  in question.  
         [0026]    [0026]FIG. 3 is a data tree showing the bit-wise encoding process of a symbol under a given prefix A. The symbols and values shown in this figure are exemplary and in no way limiting. This particular data tree is based upon values and symbols used in the order 1 table  210  shown in FIG. 2 that apply to a string beginning with the prefix  215   
         [0027]    “A”. Further, a symbol is represented by binary bits b 2 b 1 b 0  and the following binary representations for the symbol set {A, B, C, D, E, F, G, H} are assumed:  
                                                   Symbol   Value (b 2  b 1  b 0  )                           A   000           B   010           C   011           D   110           E   001           F   100           G   101           H   111                      
 
         [0028]    This binary representation is exemplary and in no way limiting. Different trees may be obtained when the symbols are represented by other binary values.  
         [0029]    The data tree  300  is a binary tree that is designed to be read from the top down. The root  305  contains the full set of symbols (all possible symbols in a given application). A fork node (such as  310 ,  320 ,  330 ,  340 ,  350 , or  360 ) contains a subset of the symbols. The terminal nodes are called leaf nodes, each of which containing a single, different symbol from the full set of symbols. A branch to the left of a node is called a Zero group, and a group to the right is called a One group. A Zero group is associated with a branch marked by a 0 bit value. A One group is associated with a branch marked by a 1 bit value. Each branch is associated with a floating-point number which represents the probabilities of the symbols in the down-linked node, which is either a Zero group or a One group.  
         [0030]    A binary data tree  300  is built in three steps:  
         [0031]    1. A partition bit is chosen for each node, starting from the root node.  
         [0032]    2. All symbols are partitioned (including Miss symbols) at each node into a Zero group and a One group. The partitioning is based on the value of a symbol at the partition bit chose in step 1. Partitioning is performed bit wise, ending at the leaf nodes, at which point a single symbol is encoded.  
         [0033]    3. A probability is assigned for each branch in the tree.  
         [0034]    A particular partition bit is chosen so as to maximize the imbalance of the probability sums of the Hit symbols (excluding the ESC symbols) in the resulting Zero and One groups. The partition bit must be one of the binary bits in the binary representation of the symbols. For example, in this figure, the partition bit must be either b 2 , b 1 , or b 0 . If a bit has been used in a parent node, then it cannot be reused in the nodes downwards. If a partition bit leads to either a Zero or a One group that contains only Miss symbols, then the use of this bit should be delayed until all other remaining bits also lead to the same effect. If a node contains only a single Hit symbol, then the partition bit is chosen to maximize the probability sums of all symbols (including both Hit and Miss) in the group containing the Hit symbol. If a node contains no Hit symbol, then the partition bit is chosen to maximize the imbalance of the Miss symbols in the resulting Zero and One groups.  
         [0035]    Partition of the symbols of a node into Zero and One is based on the value of a symbol at the chosen partition bit. Symbols with a 0 value at the partition bit are put into the Zero group and those with a 1 value at the partition bit are put into the One group. Hit symbols play a primary role in determining the partition bit for a given node. However, once the partition bit is chosen, all symbols in the node, (including Hit or Miss) are partitioned together using the same partition method.  
         [0036]    After the partition process is completed, the final step of building the binary tree involves assigning a probability value to each branch in the tree. The probabilities of the left and right branches of each node must sum to 1. The probabilities for left and right branches of a node are assigned at the same time. The assignment is done in two steps. First, the probabilities of the Hit symbols is summed for the Zero group and One group respectively. The following example is for two sums, Z p  and O p . If one or both of Z p  and O p  are zero, then the Z p  and O p  are recomputed by summing the probabilities of all (Hit and Miss) symbols in the Zero and One groups respectively. The probability for the left branch is given by Z p /(Z p +O p ); the probability for the right branch is given by Z p /(Z p +O p ).  
         [0037]    The binary data tree  300  is constructed using values and probabilities found in table  210 . The root node  305  includes the full set of symbols (in this case, {A, B, C, D, E, F, G, H}), among which A, B, C, and D are Hit symbols and E, F, G, and H are Miss symbols. This full set of symbols is partitioned into Zero and One groups based on the value of b 2 . The Zero group at node  310  includes A, B, C, and E because the b 2  bits of these symbols are 0. The One group at node  320  includes D, F, G, and H because the b 2  bits of these symbols are 1. b 2  is chosen for the first partition is because the resulting probability sum Z p  of Hit symbols (A, B, C) in the Zero group is 0.9 and the probability sum O p  of Hit symbols (D) in the One group is 0.07. This is the most unbalanced result, given that b 1  leads to a partition of 0.65 (A, E, F, G for Zero group) and 0.32 (B, C, D, H for One group), and b 0  leads to a partition of 0.87 (A, B, D, F for Zero group) and 0.10 (C, E, G, H for One group). Moving down the tree, node  310  is partitioned with the b 0  bit. Node  320  can be partitioned at either b 1  or b 0  because the resulting trees have the same probability values. The b 1  bit leads to a Zero group including only Miss symbols (F and G), while b 0  bit leads to a One group including only Miss symbols (G and H). To avoid ambiguity, the bit with the higher position (i.e., on the left), is chosen.  
         [0038]    The branching probabilities in binary tree  300  are obtained as follows. The Zero group of Node  305  is node  310 . This node  310  includes A, B, and C as Hit symbols. The One group of Node  305  is node  320 . The only Hit symbol in Node  320  is D. Probability values for these node are found in Table  210 . The probability sum Z p  of the Hit symbols in the Zero group at node  310  is 0.65+0.15+0.1 (the probability of A, B and C is 0.65, 0.15, and 0.1, respectively). The probability sum O p  of the Hit symbols in the One group at Node  320  is 0.07, given that D has a probability of 0.07. Therefore, the left branch of Node  305  has a probability of Z p /(Z p +O p )=0.9278, and the right branch has a probability of O p /(Z p +O p )=0.0722.  
         [0039]    Node  360  is a One group of node  320 . When Node  360  is partitioned at b 0 , the resulting One group includes a single Miss symbol (H). Therefore, in calculating the probability sums, both Miss and Hit symbols are used. In this case, Z p =0.07 and O p =0.0075, leading to a probability of 0.9032 for left branch and a probability of 0.0968 for right branch probability. Other nodes are handled similarly.  
         [0040]    Encoding a symbol X under a given prefix is done in three steps:  
         [0041]    1. Build the binary tree based on the prediction table of the given prefix.  
         [0042]    2. Identify the path from the root to the symbol X.  
         [0043]    3. Encode each of the probabilities on the path.  
         [0044]    For example, in this figure, symbol D is encoded with three probabilities 0.0722, 0.8378, and 0.9032, while E is encoded with 0.9278, 0.1111, and 0.0698. Each probability value is encoded using standard arithmetic encoding method.  
       Method of Use  
       [0045]    [0045]FIG. 4 is a flow diagram showing a method of data compression using prefix prediction encoding.  
         [0046]    The method  400  is performed by a system  100 . Although the method  400  is described serially, the steps of the method  400  can be performed by separate elements in conjunction or in parallel, whether asynchronously, in a pipelined manner, or otherwise.  
         [0047]    At a flow point  405 , the system  100  is ready to commence a method of data is compression using prefix prediction encoding.  
         [0048]    In a step  410 , a command is given to compress a particular set of data  150 . In a preferred embodiment, this command may either be a manual request by a user or may be automatically implemented.  
         [0049]    In a step  415 , the computer program  140  performs a set of instructions so as to re-order the particular set of data  150 . For example, a set of two dimensional data may be re-ordered into a single dimension.  
         [0050]    In a step  420 , the computer program  150  performs a set of instructions so as to alter the sequence of the data  150  using a Burrows-Wheeler transform and a Move-to-front transform. Altering the sequence of the symbols included in the data changes the probabilities of distribution and causes input values to be replaced by a positional index.  
         [0051]    In a step  425 , the re-ordered and transformed data  150  is stored in a memory.  
         [0052]    In a step  430 , the computer program  140  generates prediction probability tables for each symbol in the re-ordered and transformed data  150 . The tables are conditioned upon the prefixes of the symbol. In other preferred embodiments, the probability tables are based upon historical probability values.  
         [0053]    In a step  435 , the computer program  140  generates a binary tree structure, in such a way as to maximize the imbalance of the probability sums of the Hit symbols (excluding the Miss symbols) in each pair of the Zero and One groups, as shown in FIG. 3. Each symbol is represented by a unique path connecting the root to the symbol. symbol. The path consists of branches, each of which is assigned a conditional probability value. Encoding a symbol is done by encoding the probability values on the path from the root to the symbol.  
         [0054]    In a step  440 , the computer program  140  traverses the binary tree structure of the prefix of a symbol to be encoded and encodes the probabilities on the path from the root of the tree to the symbol. In preferred embodiments, the probability values are encoded using the arithmetic encoding method. This step may occur multiple times, with different prefixes and different strings until an entire data set is encoded.  
       Alternate Embodiments  
       [0055]    Although preferred embodiments are disclosed herein, many variations are possible which remain within the concept, scope, and spirit of the invention, and these variations would become clear to those skilled in the art after perusal of this application.