KR20060028750A - Huffman coding and decoding - Google Patents

Abstract

A method of decoding a bitstream encoded according to a Huffman coding tree of height H comprising: extracting a first codeword of H bits from the bitstream; modifying the codeword by shifting it by a first shift value; using this modified codeword to identify using at least a first data structure either a symbol or a second data structure having an associated second offset value and an associated second shift value; and if a second data structure is identified using the first data structure: modifying the codeword by subtracting the second offset value and shifting the result by the second shift value; and using this modified codeword to identify using the second data structure either a symbol or a third data structure having an associated third offset value and an associated third shift value.

Description

Huffman coding and decoding

Embodiments of the present invention relate to Huffman coding and decoding. In particular, embodiments of the present invention relate to improved mechanisms for encoding and decoding and an improved representation of a Huffman tree.

In digital processing, where a message includes a series of symbols, each individual symbol may be represented as a separate binary codeword. Huffman's algorithm uses a table of the frequency of occurrence of each symbol in the message and optimizes variable length codewords so that the most frequent codewords have the shortest length. This results in data compression and Huffman coding is commonly used in audio and video compression coding, for example MPEG.

Bulletin 1098-1101, IRE 40 (1952), by David A Huffman, "Method for Constructing Minimum-Duplicate Codes" introduces Huffman coding.

Then if there are nine symbols S0, S1 ... S8 with each occurrence frequency 5, 5, 6, 1, 2, 3, 16, 9, 9, they are shown in Figure 1 using the Huffman algorithm It can be encoded as a binary tree.

The tree 10 includes internal nodes Fi and leaf nodes Si arranged in H levels. Each leaf node is dependent from a single internal node on the second lowest level and represents a symbol. Each internal node is dependent from a single internal node on the second lowest level. The level L of a node is defined by setting the root node to level 0 and the other nodes have one level higher than the level of the node to which it depends. The highest level is the height H of the Huffman tree. The symbols (ie leaves of T) are represented from left to right as S0, S1, S2 ... S8.

The Huffman tree shown in FIG. 1 results in the encoding of the following symbols.

symbol Codeword S0 000 S1 001 S2 010 S3 01100 S4 01101 S5 0111 S6 10 S7 110 S8 111

In its simplest representation, a Huffman binary tree of height H can be represented using one word for each node of the tree. The size of this representation makes searching difficult during decoding.

IEEE Memory for Communications, Volume 43, No. 10, 2576-, Hashemian, October 1995, "Memory Efficient and Fast Search Huffman Coding," reduces the storage space required to represent Huffman trees and reduces the tree size. Increase the decoding speed. A lean single-sided growth Huffman tree is created and the Huffman tree is divided into smaller and less lean clusters (sub-trees), each at L levels apart. A super-tree is constructed, where each cluster is represented by a node. Super table specifies the super-tree. It specifies, for each node, the length of the cluster associated with the node and the address of a lookup table for the cluster. The negative entry in the lookup table is the criterion behind the super-table. A positive entry indicates that a symbol was found and the size of the entry provides the location of the symbol in memory, the codeword and the codeword length.

Inform Process Lett. 69 (1999) 119-122, "Memory-Efficient and Fast Huffman Decoding Algorithm" by Chen, whose weight is the number of leaves in the complete tree below the node. Is provided on the same leaf node. It depends on the level of the node in the tree. Every leaf node is assigned the same number and its own weight as the cumulative weight of all the leaves appearing before it. The codeword is provided with the same cumulative weight as if it were a node on the tree. Actual cumulative weights are searched to determine if one matches the same cumulative weight. If there is a match and the weights of the matching nodes are the same, the codeword is a leaf node (ie a symbol) of the tree.

Inform Process Lett., 81 (2002), 305-308, Chowdhury et al, "Efficient Decryption Techniques for Huffman Codes," all leafs to improve memory usage and search speed. Cut the Huffman tree by removing it.

It would be desirable to provide an alternative representation of the Huffman binary tree and an improved Huffman decoding mechanism for decoding the received string of binary digits.

According to an embodiment of the present invention, in a method of decoding a bitstream encoded according to a Huffman coding tree having a height of H,

Extracting a first codeword of H bits from the bitstream;

Changing the codeword by shifting the codeword by a first shift value;

Using the modified codeword to identify a second data structure or symbol having an associated second offset value and associated second shift value using at least one first data structure; And

If a second data structure is identified using the first data structure:

Changing the codeword by subtracting the second offset value and shifting the result by the second shift value; And

A method is provided that includes using the modified codeword to identify a third data structure or symbol having an associated third offset value and an associated third shift value using the second data structure.

According to another embodiment of the present invention, in a method of decoding a bitstream encoded according to a Huffman coding tree having a height of H,

Extracting a codeword of H bits from the bitstream;

Shifting the codeword by a predetermined shift value; And

A method is provided that includes using the modified codeword to identify a symbol using at least one first data structure.

According to another embodiment of the present invention, in a decoder for decoding a bitstream encoded according to a Huffman encoding tree having a height of H,

A plurality of Huffman coding trees having a height of at least H comprising at least a first data structure having an associated first offset value and an associated first shift value and a second data structure having an associated second offset value and an associated second shift value; A memory for storing data structures; And

Operable to subtract a current offset value from a codeword of H bits obtained from the bitstream, operable to shift the result by the associated shift value, and use the result to address the associated data structure A decoder is provided that includes a possible processor.

According to another embodiment of the present invention, in a method of decoding a bitstream encoded according to a Huffman coding tree having a height of H,

Storing a first data structure containing a value for each possible node at the first level of the tree;

Storing a second data structure containing a value for each possible node in a first booty at a second lower level of the tree;

Extracting a first codeword of H bits from the bitstream;

Converting the value of the first codeword to a first node location in the tree at a first level in the tree;

Accessing the first data structure to obtain a value corresponding to the first node location, the value representing the second data structure;

Converting the value of the first codeword to a second node location in the first booty at a second level of the tree; And

Accessing the second data structure to obtain a value corresponding to the second node location.

According to another embodiment of the present invention, in a method of decoding a codeword from a bitstream,

Receiving an indication of a Huffman tree as a plurality of ordered data structures, wherein the plurality of ordered data structures are associated with an identified first level L1 of the tree and each entry is complete at the identified first level. A first data structure comprising a plurality of data entries corresponding to nodes of a tree and an identified second level L2 of the tree and an identified first booty, wherein each entry is at the second identified level And, if complete, including at least one second data structure comprising a plurality of data entries corresponding to the node of the first booty;

Obtaining a value for a first level L1 in the Huffman tree;

Identifying the node at the first level (L1) of the tree, corresponding to the first L1 bits of a codeword, in a complete case;

Obtaining a data entry for the identified node from the first data structure, identifying an additional data structure if the identified node is an internal node and otherwise identifying a symbol; And

If the identified node is an internal node:

Obtaining a value for a second level (L2) in the Huffman tree, which is a level higher than the first level (L1);

Obtaining a value identifying the first booty;

Identifying the node at the second level (L2) of the first booty, in a complete case, corresponding to the first L2 bits of the received bitstream;

Obtaining a data entry for the identified node from the additional data structure that identifies an additional data structure if the identified node is an internal node and otherwise identifies a symbol.

According to another embodiment of the invention, data representing a Huffman coding tree comprising leaf nodes and inner nodes arranged at H levels, each leaf node being dependent from a single inner node on the second lowest level and Wherein each leaf node represents a symbol and each internal node is dependent on a single internal node on the second lowest level, the data being:

For each of the nodes within the first specific level of the tree, a first data structure identifying a symbol for each leaf node and an additional data structure for each inner node, including a second data structure for a first inner node. ;

At least one second data structure identified by the first data structure, for each of the nodes in the bootee, dependent from the first internal node and at a second particular level of the tree, if any At least one second data structure identifying a symbol for the node and an additional data structure for an internal node; And

Data is provided that includes at least the first level, the second level, and data specifying the first internal node.

According to another embodiment of the present invention, in a method for representing a Huffman binary tree,

Generating a first data structure associated with the identified first level L1 of the tree and comprising a plurality of entries, each entry corresponding to a node of a complete tree at the identified first level, wherein the node is Identifying an additional data structure if it is an internal node, otherwise identifying a symbol; And

Generating at least one additional data structure associated with the identified second level (L2) of the tree and associated with the identified first booty and comprising a plurality of data entries, each entry identified by the second identified A method is provided that corresponds to a node of the first booty if complete at level L2 and identifies an additional data structure if the node is an internal node and otherwise identifies a symbol.

One advantage associated with embodiments of the present invention is that the technique uses the probability of occurrence of codewords. Codewords that occur more frequently will be decoded first.

Another advantage associated with embodiments of the present invention is the low processing overhead associated with decryption, where there is at most one subtraction, one shift and one comparison at each decryption iteration. Therefore, the decoding can be implemented very efficiently in a digital signal processor (DSP).

Another advantage associated with embodiments of the present invention is that the maximum search can be designed to be less than log ₂ N.

For a better understanding of the embodiments of the invention and to understand how embodiments of the invention may be practiced, only the accompanying drawings will now be referred to by way of example.

1 illustrates a Huffman binary tree.

2 shows a device usable as an encoder and / or a decoder.

3 shows a decryption process.

4 shows another Huffman tree.

encoding

In this example, assume that there are nine symbols S0, S1, ..., S8 with each of the following occurrence frequencies 5, 5, 6, 1, 2, 3, 16, 9, 9. They can be encoded into the binary tree shown in FIG. 1 using the Huffman algorithm.

This Huffman tree can be represented as a sequence of ordered data structures as defined below in the lookup tables (Tables 2, 3 and 4) below.

Lookup table Offset_value Shift_value Sub-table Lookup Table 0 0 2 0 Lookup Table 1 12 0 One

Sub-table 0 y 0 One 2 3 4 5 6 7 symbol_locate -> S0 -> S1 -> S2 -> Sub-Table 1 -> S6 -> S6 -> S7 -> S8

Subtable 1 y 0 One 2 3 symbol locate -> S3 -> S4 -> S5 -> S5

The first data structure (Table 2) is a first lookup table. It identifies the offset_value and shift_value pairs to be used with each identified sub-table. In this example, it indicates that shift_value of 0 offset and 2 should be used with sub-table 0 (Table 3) and offset_value of 12 and shift_value of 0 should be used with sub-table 1 (Table 4).

The second data structure (Table 3) is a lookup table. It is addressed using the value y and in return provides a value for symbol_locate. The value for symbol_locate may indicate a symbol value or another lookup table. For example, values for y equal to 0, 1, 2, 4, 5, 6, 7 indicate symbols S0, S1, S2, S6, S6, S7, S8 and values for y equal to 3, respectively. Indicates sub-table 1 (Table 4).

The third data structure (Table 4) is a lookup table. It is addressed using the value y and in return provides a value for symbol_locate. The value for symbol_locate may indicate a symbol value or another lookup table. In this example, values for y equal to 0, 1, 2, 3 indicate symbols S3, S4 S5, S5, respectively.

The 8-bit symbol_locate may be formatted to identify whether its most significant bit (MSB) is a pointer to a symbol (MSB = 0) or another lookup table (MSB = 1). Bits 1-7 provide the address of the correct symbol or lookup table. For example, the value of symbol_locate in sub-table 0 at y = 3 would be 1000 0001 indicating sub-table 1. The value of symbol_locate in sub-table 0 at y = 1 will be 0000 0000 representing symbol S0 according to Table 5 below.

symbol locate symbol 0000 0000 S0 0000 0001 S1 0000 0010 S2 0000 0011 S3 0000 0100 S4 0000 0101 S5 0000 0110 S6 0000 0111 S7 0000 1000 S8

The generation of the data structures described above will now be described. Table 6 shows the methodology used to generate the data structures.

In Table 6, column 1 lists the symbols Si in order for i = 0, 1, 2... Column 2 lists its codewords adjacent to each symbol. Column 3 provides a count value Count _Si for each codeword.

Count _Si is the value of the sequence of bits obtained by adding 1s to the codeword for symbol Si until the codeword for symbol Si has a length H. For example, the count value for S0 is a value of 00011 (2 + 1), and the count value for S2 is a value of 01011 (8 + 2 + 1). Alternatively, the count value Count _Si may be calculated for each symbol Si occupying the codeword and level L _i of the value V, as [(V + 1) * 2 ^ (HL _i )] − 1. For example, for S3 {01100} V = 12 & L = 0 and count = [(12 + 1) * (2 ^ 0)]-1 and for S8 {111} V = 7 & L = 2 , And count = [(7 + 1) * (2 ^ 2)]-1 = 31.

Column 4 provides an argument for each symbol. This is calculated for symbol Si as count _Si −count _Si −1 when count _S −1 = −1. It can alternatively be calculated as 2 ^ (HL _i ), for the symbol Si at level Li.

Column 5 provides a 'shift' for each symbol. It is the logarithm to base 2 of the argument of the symbol. The shift can alternatively be calculated for each symbol Si as L _i .

One 2 3 4 5 6 7 8 9 Si Codeword Count _si Argument 2 ^ (HL _i ) Shift HL _i y = (x-0) >> 2 y = (x-12) >> 0 S-1 -One S0 000 3 (011) 4 2 0 (0) - S1 001 7 (111) 4 2 1 (1) - S2 010 11 (1011) 4 2 2 (10) - S3 01100 12 (1100) One 0 3 (11) 0 S4 01101 13 (1101) One 0 3 (11) One S5 0111 15 (1111) 2 One 3 (11) 3 S6 10 23 (10111) 8 3 5 (101) - S7 110 27 (11011) 4 2 6 (110) - S8 111 31 (11111) 4 2 7 (111) -

Equation 1 is used to calculate the values in columns 6 and 7 which provide the content for the second and third data structures (Tables 3 and 4).

y = (x-offset_value) >> (shift_value)

X is a codeword value, offset_value is an integer greater than or equal to 0, and shift_value is an integer greater than or equal to 0. The operator " >> " indicates that the value (x-offset_value) should be truncated by shift_value to lose its least significant shift_value. The shift to the left is equivalent to the division by 2 ^ shift_value, but it is easily performed by the digital signal processor DSP.

The offset_value is set to 0 and the shift_value is set to 2 for column 6, that is, the second data structure (Table 3). The equation y = (x-0) >> 2 is used to calculate each of the entries in column 6, corresponding to the y values in sub-table 0 (Table 3). The symbols S3, S4 and S5 share a common y value. An additional sub-table is used for the symbols.

For column 7, ie the third data structure (Table 4), the offset_value is 12 and the shift_value is set to zero. Equation y = (x-12) >> 0 calculates each of the entries in column 7 for unresolved symbols S3, S4 and S5 corresponding to y values in sub-table 1 (Table 4) Used.

Thus, the sub-table 0 represents nodes in the Huffman binary tree of FIG. 1 at level Li, i.e. Li = H-shift_value, which are shift_value levels removed from the top of the tree.

The nodes at L = 3 are S0, S1, S2, F2, empty, empty, S7, S8. The empty nodes will be dependent from the leaf node associated with symbol S6. Therefore, the symbol S6 is placed in the dependent empty nodes. Nodes at L = 3 may be rewritten as S0, S1, S2, F2, S6, S7, S8. This corresponds to the content of the entries in sub-table zero.

The internal node F2 is the root of Booty. The sub-table 1 represents the booties. The count value of any leaf nodes dependent from F2 will have values between 12 and 15. The count values of the codewords are renormalized by subtracting the offset value for 12, sub-table 1.

The sub-table 1 represents the nodes of the sub-tree at level L in the Huffman binary tree equal to H-shift_value. Shift_value for sub-table 1 is 0 for the sub-tree, so L = 5.

Nodes at L = 5 are S3, S4, empty, empty in order. The empty nodes will be dependent from the leaf node associated with symbol S5. The symbol S5 is therefore placed in the dependent empty nodes. Nodes at L = 5 may be rewritten as S3, S4, S5, S5. This corresponds to the content of entries in sub-table 1.

Huffman tree in FIG. 1 is therefore represented by a first data structure representing the tree at level L = 3, a second data structure representing sub-tree at sub-table 0 and a level L = 5, sub-table 1.

Sectioning the tree is necessary to allow the most promising symbols to be found first in an efficient manner. However, the introduction of too many sections requires additional processing steps to use additional memory to store additional sub-tables and additional shift and offset values and to decode less commonly occurring symbols.

For example, it is possible to indicate the Huffman tree by sectioning the Huffman tree at levels other than L = 3 and L = 5. For example, if the tree is sectioned at L = 3, L = 4 and L = 5, there will be three sub-tables. The first entry of the sub-table for L = 4 will refer to the sub-table for L = 5 and the second entry will refer to S5. The first entry of the sub-table for L = 5 will refer to S3 and the second entry will refer to S4. The offset for both the sub-tables is 12. The shift for the sub-table for L = 4 is 1 and the shift for the sub-table for L = 5 is 0.

The following should be mentioned for the sectioning of the Huffman tree of FIG. 1 which provides the data structures of Tables 2, 3, 4 and 5.

The data structure representing the level L of the tree (ie the tree sectioned in L) has the same shift value as H-L. If the node N has a codeword value V and is at level L, the data structure referenced from node N in the tree has offset_value V * 2 ^ (H-L).

For the sub-table 0, the shift_value is set equal to H-L *, where L * is the level at which the tree is sectioned. Here it is the lowest level at which multiple leaves appear. In Figure 1 there is one leaf at L = 2, but there are multiple leaves at L = 3. Therefore the tree is sectioned at L = 3 and the shift_value = 2. The offset_value is zero.

For example, the sub-table 1 is referenced via node {011} at L = 3. Therefore, V = 3 and the offset_value for the sub-table 1 is 3 * 2 ^ 2. The shift value for the sub-table 1 is set equal to H-L *, where L * is the level at which the tree is sectioned. Here, it is the lowest level at which multiple leaves appear in the sub-tree. In FIG. 1, the sub-tree has F2 as its root at level L = 3. The sub-tree has one leaf at L = 4, but has two leaves at L = 5. Thus the tree is sectioned at L = 5 and shift_value = 0.

2 shows a device 20 operable as an encoder. The encoder device includes a processor 22 and a memory 24. The memory 24 stores computer program instructions for controlling the processor 22 to perform the encoding process described above.

The computer program instructions may be sent to the memory via a suitable storage medium on which the instructions are implemented or they may be sent via electrical signals implementing the instructions.

The processor 22 has an input 21 for receiving data for encoding and an output 23 for providing the encoded data. The encoded data includes a plurality of data structures representing a Huffman tree and a value for the height H of the tree.

Decrypt

2 shows a device 20 operable as a decoder. The decoder includes a processor 22 and a memory 24. The memory stores data structures representing the Huffman tree as described above. For example, the memory 24 may store tables corresponding to those shown in Tables 2, 3, 4, and 5 above. The memory also stores computer program instructions for controlling the processor 22 to perform the decryption process described below with reference to FIG.

The computer program instructions may be sent to the memory via a suitable storage medium on which the instructions are implemented or they may be sent via electrical signals implementing the instructions.

The processor 22 has an input 21 for receiving data for decoding and an output 23 for providing the decrypted data. The height of the Huffman tree is known in the decoder. This may be passed to the decoder in a header for which data for decoding is provided.

The decoder performs the following steps as shown in FIG.

In step 100 the current sub-table identifier z is set to zero.

Then in step 102, the H bits are extracted from the bitstream, having the value x.

Then in step 104, the lookup table is accessed. The offset_value and shift_value for sub-table z are obtained.

Next, in step 106, calculate the y value for the current sub-table from Equation 1 using x and the obtained values of offset_value and shift_value for the current sub-table.

In step 108, the current sub-table, sub-table z, is accessed. Obtain symbol_locate from the sub-table z corresponding to the calculated y values.

Next, in step 110, a comparison is performed on the MSB of the obtained symbol_locate. If the MSB of the obtained symbol_locate is zero, the process jumps to step 114. If the MSB of the obtained symbol_locate is 1, the process jumps to step 112.

In step 112, the current sub-table identifier z is set equal to the remaining least significant bits of the symbol_locate obtained in step 108. The process then returns to step 104.

In step 114, a symbol corresponding to symbol_locate is obtained in step 108.

An example of the process shown will now be provided using the example lookup tables provided above (Tables 2, 3, 4 and 5). The codeword to be searched for is {0,1,1,1}. Let the extracted bits be {0,1,1,1,0}.

In step 100, set the current sub-table indicator z = 0.

In step 102, bits {0,1,1,1,0} are extracted. Therefore x = 14.

In step 104, the lookup table (Table 2) is accessed. Offset_value = 0 for sub-table 0 and shift_value = 2 for sub-table 0.

In step 106, y is calculated using Equation 1.

y = (x-0) >> 2 = 3

In step 108, access the current sub-table, sub-table 0 (Table 3). Obtain symbol_locate from sub-table 0 corresponding to the calculated y value. The symbol_locate is {1000 0001}.

In step 110, since the MSB of the obtained symbol_locate is determined to be 1, the flow goes to step 112.

In step 112, z is set equal to the remaining least significant bits {000 0001} of the obtained symbol_locate, i.e., z = 1.

In step 104, the current lookup table (Table 2) is accessed. Obtain a new offset_value and a new shift_value for the new current sub-table (sub-table 1). Offset_value = 12 for sub-table 1 and shift_value = 0 for sub-table 1.

In step 106, y is computed for the current sub-table, sub-table 1, using equation (1). y = (x-12) >> 0 = 2

In step 108, the current sub-table (sub-table 1) is accessed. Obtain symbol_locate corresponding to the new y value (y = 2). The symbol_locate is {0000 0101}.

In step 110, the MSB of the obtained symbol_locate is determined to be zero, and therefore, step 114 is reached.

In step 114, a symbol corresponding to the obtained symbol_locate is obtained. The symbol corresponding to the obtained symbol_locate {0000 0101} is S5 from Table 5.

It will be appreciated that the same result will be achieved if the extracted bits are {0,1,1,1,1} instead of {0,1,1,1,0}.

Additional explanation

As a further description the encoding of the Huffman tree shown in FIG. 4 will now be briefly described.

Table 7 is generated:

Si Codeword count _Si S0  000 15 S1  001 31 S2  010 47 S3  01100 51 S4  0110100 52 S5  0110101 53 S6  011011 55 S7  0111 63 S8  10 95 S9  110 111 S10  111 127

Sectioning the tree at L = 3 gives y = (x-0) >> 4.

y0 0 One 2 3 4 5 6 7 symbol_locate S0 S1 S2 Go to table 1 S8 S8 S9 S10

Sectioning the tree at L = 4 gives y = (x-48) >> 3, where V {011} * 2 ^ 4 = 48.

y1 0 One symbol_locate Go to table 2 S7

Sectioning the tree at L = 5 gives y = (x-48) >> 2, where V {0110} * 2 ^ 3 = 48.

y2 0 One symbol_locate S3 Go to table 3

Sectioning the tree at L = 7 gives y = (x-52) >> 0, where V {01101} * 2 ^ 2 = 52.

y3 0 One 2 3 symbol_locate S4 S5 S6 S6

Although the present invention has been described with reference to various specific examples, it should be understood that various modifications and changes may be made without departing from the spirit and scope of the invention.

Claims (41)

A method of decoding a bitstream encoded according to a Huffman coding tree having a height of H, Extracting a first codeword of H bits from the bitstream; Changing the codeword by shifting the codeword by a first shift value; Using the modified codeword to identify a second data structure or symbol having an associated second offset value and associated second shift value using at least one first data structure; If a second data structure is identified using the first data structure: Changing the codeword by subtracting the second offset value and shifting the result by the second shift value; And Using the modified codeword to identify a third data structure or symbol having an associated third offset value and an associated third shift value using the second data structure. 2. The method of claim 1, further comprising accessing a lookup table to obtain the first shift value and accessing the lookup table to obtain the second offset value and the second shift value. How to. 3. The method of claim 1 or 2, wherein the first data structure represents a first level of the Huffman coding tree and the second data structure represents a second lower level of the Huffman coding tree. 4. A method as claimed in any preceding claim, wherein at least the value of the height H, the first shift value, the second offset value, the second shift value, the first data structure and the second data structure. The method further comprises the step of receiving. 5. The method of any one of claims 1 to 4, wherein the step of changing the codeword by shifting the codeword by a first shift value, if any, first subtracts a first offset value from the codeword and as a result Shifting by the first shift value. A computer program for performing the method of any one of claims 1 to 5. A storage medium or transmission medium embodying the computer program of claim 6. A method of decoding a bitstream encoded according to a Huffman coding tree having a height of H, Extracting a codeword of H bits from the bitstream; Shifting the codeword by a predetermined shift value; And Using the modified codeword to identify a symbol using at least one first data structure. 8. The method of claim 7, further comprising accessing a lookup table to obtain the predetermined shift value. 10. The method of claim 8 or 9, wherein the first data structure represents a first level of the Huffman coding tree. 11. The method of any one of claims 8 to 10, further comprising receiving a value of at least height H, the predetermined shift value and the first data structure. 12. The method according to any one of claims 8 to 11, wherein the step of shifting the codeword by a predetermined shift value, if any, first subtracts a first offset value from the codeword and results in the predetermined shift value. Shifting by as much as possible. A computer program for performing the method of any one of claims 8 to 12. A storage medium or transmission medium embodying the computer program of claim 13. A decoder for decoding a bitstream encoded according to a Huffman coding tree having a height of H, A plurality of Huffman coding trees having a height of at least H comprising at least a first data structure having an associated first offset value and an associated first shift value and a second data structure having an associated second offset value and an associated second shift value; A memory for storing data structures; And Operable to subtract a current offset value from a codeword of H bits obtained from the bitstream, operable to shift the result by the associated shift value, and use the result to address the associated data structure A decoder comprising a processor capable of. 16. The decoder of claim 15, wherein the first data structure represents a first level of the Huffman coding tree and the second data structure represents a second lower level of the Huffman coding tree. 17. The decoder of claim 16, wherein the first shift value corresponds to the first level. 18. The decoder of claim 16 or 17, wherein the second shift value corresponds to the second level. 19. The decoder of any one of claims 16-18, wherein the second offset value identifies a location of a first sub-tree in the Huffman tree. The processor of claim 17, wherein the processor obtains a value from addressing the associated data structure, and then performs a comparison using the value and uses the value according to the comparison. A decoder operable to identify a symbol or a new current offset value. 21. The decoder of claim 20 wherein the comparison uses the most significant bit (MSB) of the value. 22. The decoder of claim 20 or 21, wherein the current offset value is initially set to the first offset value. A method of decoding a bitstream encoded according to a Huffman coding tree having a height of H, Storing a first data structure containing a value for each possible node at the first level of the tree; Storing a second data structure containing a value for each possible node in a first booty at a second lower level of the tree; Extracting a first codeword of H bits from the bitstream; Converting the value of the first codeword to a first node location in the tree at a first level in the tree; Accessing the first data structure to obtain a value corresponding to the first node location, the value representing the second data structure; Converting the value of the first codeword to a second node location in the first booty at a second level of the tree; And Accessing the second data structure to obtain a value corresponding to the second node location. A computer program for performing the method of claim 23. A storage medium or transmission medium embodying the computer program of claim 24. In the method of decoding a codeword from a bitstream, Receiving an indication of a Huffman tree as a plurality of ordered data structures, wherein the plurality of ordered data structures are associated with an identified first level L1 of the tree and each entry is complete at the identified first level. A first data structure comprising a plurality of data entries corresponding to nodes of a tree and an identified second level L2 of the tree and an identified first booty, wherein each entry is at the second identified level And, if complete, including at least one second data structure comprising a plurality of data entries corresponding to the node of the first booty; Obtaining a value for a first level L1 in the Huffman tree; Identifying the node at the first level (L1) of the tree, corresponding to the first L1 bits of a codeword, in a complete case; Obtaining a data entry for the identified node from the first data structure, identifying an additional data structure if the identified node is an internal node and otherwise identifying a symbol; And If the identified node is an internal node: Obtaining a value for a second level (L2) in the Huffman tree, which is a level higher than the first level (L1); Obtaining a value identifying the first booty; Identifying the node at the second level (L2) of the first booty, if complete, corresponding to the first L2 bits of the received bitstream; Obtaining a data entry for the identified node from the additional data structure that identifies an additional data structure if the identified node is an internal node and otherwise identifies a symbol. A computer program for performing the method of claim 26. A storage medium or transmission medium embodying the computer program of claim 27. Data representing a Huffman coding tree comprising inner nodes and leaf nodes arranged at H levels, each leaf node being subordinated from a single inner node on the second lowest level and each leaf node representing a symbol and each inner The node is data dependent from a single internal node on the second lowest level, the data being: For each of the nodes within the first specific level of the tree, a first data structure identifying a symbol for each leaf node and an additional data structure for each inner node, including a second data structure for a first inner node. ; At least one second data structure identified by the first data structure, for each of the nodes in the bootee, dependent from the first internal node and at a second particular level of the tree, if any At least one second data structure identifying a symbol for the node and an additional data structure for an internal node; And Data specifying at least the first level, the second level, and the first internal node. 30. The data of claim 29, wherein the first data structure, if present, identifies a symbol for each empty node. 31. The data of claim 29 or 30, wherein the second data structure identifies a symbol for each empty node of the bootie at a second level of the tree. 32. The data of any of claims 29 to 31, wherein the first level is the lowest level in the tree with at least two leaf nodes. 33. The data of any of claims 29-32, wherein the second level is the lowest level in the bootley with at least two leaf nodes. 34. The method according to any one of claims 29 to 33, wherein at the level L (L = 0, 1, 2 ..) and with the value V, the first internal node depends on V * 2 ^ (HL). Data characterized by the value to be specified. 35. The data of any of claims 29 to 34, further comprising data specifying H. 36. A storage medium or transmission medium embodying data according to any of claims 29-35. In the way to represent a Huffman binary tree, Generating a first data structure associated with the identified first level L1 of the tree and comprising a plurality of entries, each entry corresponding to a node of a complete tree at the identified first level, wherein the node is Identifying an additional data structure if it is an internal node, otherwise identifying a symbol; And Generating at least one additional data structure associated with the identified second level L2 of the tree and associated with the identified first booty and comprising a plurality of data entries, wherein each entry is identified by the second identified If complete at level (L2), identifying an additional data structure corresponding to a node of the first booty and if the node is an internal node; otherwise identifying a symbol. 38. The method of claim 37, executing an algorithm for determining the number of data structures in the Huffman tree and the associated levels of the data structures. The method of claim 37 or 38, wherein the value dependent on V * 2 ^ (HL) is used to identify a bootie with a root node at level L (L = 0, 1, 2 ..) and value V. And further comprising a step. An encoding method and / or a decoding method substantially as described above with reference to the accompanying drawings and / or as shown in the accompanying drawings. An encoder or decoder as substantially described above with reference to the accompanying drawings and / or as shown in the accompanying drawings.

Images