CHAPTER 5 A MEMORY EFFICIENT SPEECH CODING SCHEME WITH FAST DECODING

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1 86 CHAPTE A MEMOY EFFICIENT SPEECH CODING SCHEME WITH FAST DECODING. INTODUCTION Huffman coding proposed by Huffman (9) is the most widely used minimal prefix coding algorithm because of its robustness, simplicity and variable length property. The performance of the coding depends not only on the data compression method but also depends up on the characteristics of the chosen application. Since no individual compression technique will be suitable for every application, the success of the compression technique depends up on the resource constraints such as knowledge about the type of data to be compressed, memory usage and execution speed. enato Pajarola (003, 999) discusses various issues in decoding techniques. As the decoding time cost is linearly proportional to the size of the compressed data and bounded by the number of symbols involved in the output. It requires much attention on the speed and space of the decoding technique rather than the construction of the encoding, with the increasing amount of data among the network. Further the identification of boundary position in the compressed data is another issue in the decoding. There have been very limited number of work on fast and efficient decoding rather than memory efficient and fast Huffman construction.the memory requirement and complexity of the traditional Huffman tree is O ( h ) and O (h) respectively where the Canonical Huffman tree reduces to O (h) and O (log h)

2 87 respectively through its common length sequential codeword property Manoj Aggarwal and Narayan (000). While constructing the traditional Huffman tree the sparsity of the tree gets increases when it grows from the root. It leads to tremendous wastage of memory and takes much time for traversing the tree to locate symbol (eza Hashemian 99). So the proposed scheme replaces the general Huffman tree by minimum variance Huffman tree, since its variance is very small. Also, for further improvement length restricted Huffman coding is suggested which also reduces the length of the Huffman tree there by improving the searching time and memory. Generally for the Huffman code representation and implementation the tree data structure can be used since it takes a memory complexity of O ( h ) and computational complexity of O (h) where h-is the height of the Huffman tree. The memory requirement of the proposed scheme depends up on the Huffman tree. As the decoding proposed by Manoj Aggarwal and Ajai Narayan (000) required few computations per codeword and independent of number of codeword, the proposed scheme strictly follows their decoding algorithm with a small extension of custom coding decoding. As the canonical Huffman codes reduces the memory requirement to O(h) and decoding complexity to O(log h) because of its property that all code words of a particular length are consecutive binary numbers, the proposed scheme prefers the transformation of length restricted Huffman tree into canonical Huffman tree. Also, this transformation ensures that all code words with same length have the same first bit change position which helps to easily identify the length of codeword uniquely. Hence the proposed decoding method requires very few computations with limited decoding complexity. Generally the memory requirement would be large because of the redundancy that is introduced into the decoding table. But as the proposed decoding algorithm

3 88 uses the length or level restricted Huffman table, the number of redundancy introduced will be minimum which will not affect the memory requirement. Based on the DFS manner on the Huffman tree and the level compression technique, the proposed work presents a new array data structure to represent the HT in a more compact way.. EATED WOKS eza Hashemian (99) presented an efficient decoding scheme based on clustering technique to alleviate the problem of Huffman tree sparsity with minimal search time. The memory requirement is varied from O (n) to O ( t ) with a decoding complexity of O (log n) where n-is number of codewords/leafnodes. In this, the partitioning of Huffman tree into number of smaller clusters becomes an issue, since it decides the memory requirement. Manoj Aggarwal and Ajai Narayan(000) proposed a tree clustering based algorithm for efficient Huffman decoding with a computational complexity of O (h) which is independent of the number of codeword(n),the height of the Huffman tree h or length of a codeword. In this, the Huffman tree partition is corresponding to the leading codeword. Hence the partition number uniquely determines the length of the codeword and also easily identifies the symbol, since all the code words are consecutive binary numbers because of canonical Huffman property. This method requires very few computations for decoding. But there is more possibility of memory wastage in the worst case condition. Because while transforming general Huffman tree to Canonical Huffman tree, it introduces the redundancy into the decoding table. If the number of code words in the particular partition is increased, then the redundant code words to be inserted as per CHT will be minimized. To overcome this problem, this proposed work transforms the ength restricted Huffman tree to canonical Huffman tree. In this, length of the overall tree is restricted, so that the difference between longest codeword

4 89 and shortest codeword of the particular partition will be automatically reduced to small size which automatically minimizes the number of codewords to be inserted. Ya-Jun He et al (007) proposed an efficient and fast Huffman decoding method.in this first they partition the Huffman tree into number of subtrees and then decoded them using Direct Combinational ogic based on the look up table. They concluded that the partitioning of subtrees made the decoding operation easier and faster and also better then ordinary Huffman coding. Though there are many variants of Huffman decoding,mostly all the advanced decoding methods partition the Huffman tree in order to get efficient and fast decoding. Thus the proposed speech coder also follows a Tree clustering based algorithm for fast decoding..3 POPOSED ACHITECTUE AND DESIGN The proposed length restricted Huffman speech coder with fast decoding architecture is shown in Figure.. In this first the input speech is transformed into textual words using speech recognition engine and then coded with minimum variance ength restricted Huffman coding and modified BCI algorithm as depicted in chapter. While constructing the Huffman tree, depending up on the number of symbols the sparsity of the tree progressively increases thus leads to memory wastage. To reduce the Huffman sparsity, the minimum weighted length may be subject to the restriction for all i, l i where is the constant level at which the tree must be trimmed. Milidiu et al (998) BCI algorithm has been chosen for implementation since it is relatively simple and inplace. Figure. in

5 90 previous chapter shows the sequence of length restricted Huffman tree construction. As the input list is already sorted, it takes O (n) time complexity. Input speech Microsoft Speech SDK Word Word in corpus? No Yeso MV Huffman Encoding Corpus Generation of Code for isted word Safety marking code Generator Speech Perception rate Synthesis +Text eplace code By word Canonical Huffman Decoding Custom Coding Figure. ength restricted Huffman speech coder with fast decoding The restricted Huffman with various partitions or sub trees are shown in Figure.. The proposed scheme prefers the transformation of this length restricted Huffman tree into canonical Huffman tree which helps to easily identify the length of codeword uniquely. Generally the same Huffman table can be used at both the encoding and decoding side. The proposed work strictly follows the work of Manoj Aggarwal and Ajai Narayan (000) for efficient decoding. For more efficient and quick decoding, it transforms the length restricted Huffman codes into canonical Huffman codes.

6 9 Figure. Minimum variance length restricted Huffman tree of code words Canonical Huffman codes reduce the memory requirement to O (h) and decoding complexity to O (log h), since all code words of its particular length are consecutive binary numbers. Also the canonical codes can be easily partitioned into clusters of code words of equal length.the partition number uniquely determines the length of the codeword with very less computation. Also it ensures that all code words of equal length have the same first bit change position. For example the first bit change position for the code word 000 and 000 are 3 and respectively. Once the first bit change position is known, then the length of the leading modified codeword can be determined uniquely which significantly reduces the decoding complexity.

7 9 Figure.(a) in previous chapter and Figure. shows the length unrestricted Huffman tree and length restricted Huffman tree respectively. Both trees can be viewed with several left and right sub trees attached at different levels of the tree. et S i and S i be the left and right sub tree and P i and P i represents left partition and right partition respectively, where i - level of the sub tree, left sub tree and -right sub tree. Table. (a) and (b) shows the length restricted and length unrestricted Huffman table with various partitions and sub trees. et the level at which the sub tree is connected to main tree be t. The code words corresponding to words in the sub tree S have the same first (t+) bits. t max and t max define the maximum level of the left sub tree and right sub tree respectively. First bit change position along with the first bit uniquely, determines the sub tree of the leading code word in the bit stream. The function mbc identifies the first bit change position, starting from the leading bit of input bit stream. Based on this first bit change position the general Huffman tree can be easily transformed into clusters of canonical code words. The symbols of the general Huffman tree and modified (canonical) Huffman tree are represented by small and capital letters for easy understanding. et the code word corresponding to a word x in the original length restricted Huffman table be c x and the length be len (c lx ). The partition containing the symbol word x is P x and the symbol word with the largest code word is P x by y x. For every symbol word x in the original length restricted Huffman table, all possible words with prefix c x and length len (c yx ) will be added to the modified decoding table. That is d where d=(len(c yx )-len(c x )) code words will be added and assigned to the symbol word x.

8 93 Table. ength unrestricted Huffman table Subtree Partition mbc Symbol Code Word S P S P S 3 S S P 3 P P 3 Of I This Was To And A that He Made It The S S Table. ength restricted Huffman table Subtree Partition mbc Symbol Code Word S P That I This 000 He 00 It 00 Made 0 S S 3 P P 3 3 Of Was 0 0 To S S 3 P P P P 3 3 And A (Mark) The

9 9 It is to be noticed that in the length unrestricted Huffman Table., in the first partition of the right sub tree(p ), the difference between largest code word and lowest code word is 7-3=. So it needs =6 redundancy symbols to be inserted for making the canonical Huffman code words, which leads to memory wastage. But this can be avoided through length restricted Huffman code, since it minimizes the number of additional code word to be added by reducing the over all height of the tree. The partitioning and decoding of the modified Huffman table is done as per the decoding algorithm. The code word C x corresponding to x in the modified(canonical) decoding table will have same lmbc as that of original Huffman table since c x is the prefix of C x. Decoding Algorithm. If (firstkbits (B, ) =0), then traverse the right sub tree up to maximum position, else traverse the left sub tree up to maximum position.. Get the leftmostbitchange (mbc) i of bit stream which gives partition index. 3. If leftmostbitchange i exceeds the maximum length of its sub tree length, set it to maximum length (i=t max ). Get the common length of that particular partition () from look up table.. Get the first codeword of that partition (FC) from look up table.

10 9 6. ead the number of bits from the input bit stream(c) 7. Find the numerical equivalent of the difference between the code words of bit stream read and the first code word of the identified partition. (C-FC) 8. Pick the symbol word and actual length according to the numerical equivalent from sub tree structure. 9. eft shift the bit stream by the actual length of the symbol recently identified. 0. Continue the process till the bit stream becomes empty. The Table.3 shows the modified Huffman table which contains the additional column actlen which will have the actual length of symbol words in the original Huffman table. Also two D arrays of size 3*M look up table are created for both left and right sub tree shown in the Tables. and. respectively. In these arrays, each column i of left base or right base corresponds to partition P i or P i of modified Huffman table. In this, first element becomes the actual or common length ( i ) of that partition i, second element represents the least code word FC i in P i or P i and third is a pointer to another D array O i or O i for left and right sub tree respectively. The array O i is a N i * array where N i is number of code words in the partition P i in which the first element becomes the actual symbol word and second being actual length of that word.

11 96 Table.3 Modified (canonical) length restricted Huffman table Subtree Partition MBC Symbol Codeword Actlen S P That 0000 That 000 I 000 I 00 This 000 He 00 It 00 Made 0 S P Of 0 3 S 3 P 3 3 Was 0 S P To S P And And 00 3 And 00 3 A 0 S P (mark) 00 - S 3 P 3 3 The 00 ike arithmetic coding, it need not keep symbol frequencies to decompress the original symbol. It has to refer only to these look up tables which are constructed from the modified Huffman table. Hence the decoder need not keep the symbol frequency list for the construction of Huffman tree. It reads the input stream and from the first bit change position it identifies the partition number. The total time complexity of the decoding becomes O (n+m) where m-is the length of the input bit stream to be decoded. Hence the proposed decoding method requires very few computations with limited decoding complexity.

12 97 P Table. eft sub tree data structure P P 3 3 P That Of 3 Was To That I I This He It Made Table. ight sub tree data structure P P P and 3 and 3 and 3 a O (Mark) 3 I 3 O O 3

13 98.3. Decoding Illustration et the bit stream to be decoded be B= The function first bits (B, k) returns the first k bits of bit stream B. For the input stream the first partition becomes P since the mbc is.from the lookup table. the common length of that partition is and first codeword(fc) of that partition is 0000.The numerical equivalent of difference between bits of bit stream (C) and First codeword(fc) is which is the index of actual symbol He. eft shift the bit stream by actlen and the same process will be continued till the bit stream is empty. Table.6 shows this iteration step. Finally the input bit stream is decoded as he made this. Table.6 Decoding of the bit stream (He Made This) Item Bit stream Part mbc FC C C-FC Symbol actlen P He 0000 P made P This Hence the given bit stream is he made this. The decoder bound time is proportional to the maximum length size of ength restricted codeword + where - is restricted length.. EXPEIMENTA ESUTS AND PEFOMANCE ANAYSIS.. Experimental Setup In this text coding based speech coder an efficient and fast decoding is achieved by tree clustering based decoding technique. If the Huffman tree is partitioned into number of subtrees then the decoding operation will be very easier. Because the subtree has to be decoded only based on some look up table which makes the decoding very fast. In order to simulate this decoding technique the same experimental set up depicted in

14 99 section 3.. is used. The corpus has been trained as a speaker dependant for a single speaker speech signal and constructed/coded in the form of ength unrestricted Huffman tree corpus as depicted in chapter 3 and Minimum variance ength restricted Huffman tree corpus as depicted in chapter are decoded using this tree clustering based technique. Both the tree corpuses are constructed with 0,000 most frequently used English words obtained from wikitionary list. In this proposed coder, Huffman tree becomes sparse as the tree grows in the number of levels and as a result, the memory efficiency becomes a serious issue in case of high density code words. Thus to avoid the memory wastage and fast symbol searching, the usage of length restricted coding is advisable rather than the unrestricted coding. Also, this length restricted coding is combined with tree clustering based decoding for further fast and efficient searching of symbol. The time and memory complexity of those corpuses are derived... esults and Analysis The proposed scheme transforms the decoding table of general Huffman tree in such a way that it posses the structure of canonical Huffman codes. Since the codes in the modified decoding table are similar to original list, it doesn t require any modification in the encoding side. While decoding, the general Huffman tree table is partitioned into clusters of code words of equal length as per canonical Huffman concept. Since the code words in a particular partition are consecutive binary numbers, the corresponding symbol can be identified by computing the offset of the extracted bits from the numerically least codeword in the identified partition. Normally the Huffman tree requires O ( H ) memory and a computational complexity of O (log H) where H is height of the Huffman tree (Huffman 9). Since the proposed scheme is a semi adaptive technique and

15 00 maximum height of the tree is at most + the total time complexity becomes sum of the time to compute the canonical ordering and the number of times the decoding is performed which is equivalent to O(n+m) is derived as below. Complexity of Huffman tree: ) Unlength restricted Huffman tree The number of leaf nodes in the tree is 0,000. Generally the memory requirement of the Huffman tree is O( h ) Computation Complexity is O(h), Where h is the height of the Huffman tree. In this proposed work the height of the unlength restricted Huffman tree is h is 7 for the corpus words of ) Minimum variance ength restricted Huffman tree The number of leaf nodes in the ength restricted Huffman tree is 0000 i) Time to compute Huffman tree: Complexity for creation of min heap tree with sorted n node is O(n) time The number of leaf nodes in the ength restricted Huffman tree is n Complexity for picking first minimum element is O(),second minimum element O(). Hence the decoding complexity becomes O(log n) ii) Time to compute the variant of Huffman tree: Height of the Min-Heap tree =O( log n)

16 0 Height of Huffman tree O(h)=O(n) In the canonical Huffman the tree is partitioned into left and right partition based on the leading bit.so the change in the value of bit between bit- and bit- can be measured by number of equivalent classes. So number of partitions in the tree =Number of equivalent classes. iii) The time to compute the set of partitions=o(n) DFS to compute equivalent classes time=o(n) iv) Time to compute Canonical ordering is = l+ log n n log n =O(n) Where as No.of time the decoding algorithm performed ength of given word/size of length of minimum partition m/constant =O(m) Hence the total time complexity=o(n+m) where m is the length of the input bit stream to be decoded. The Table.7 shows the comparison results of various decoders. Table..7.Complexity of Various decoders Sl. No Type of the Decoder Memory requirement Decoding complexity Huffman Tree O h O(h) Sparse Huffman tree(n is quite small compare to h O(n) O(log n) 3 Canonical Huffman tree O(h) O(log h) Minimum variance ength restricted Huffman tree O(n) O(n+m)

17 0 Thus the time required to compute the canonical order becomes O (n) and total decoding time complexity becomes O (n+m).. SUMMAY OF CONTIBUTION A new scheme which is a combination of length restricted Huffman coding and tree clustering based decoding is proposed with modification for the efficient memory storage and fast searching. Due to variable length coding, the Huffman tree gets progressively sparse as it grows from the root. This sparsity in the Huffman tree may cause tremendous waste of memory space and also results in unnecessary extensive search procedures for locating a symbol. Hence the proposed coding scheme supports length restricted Huffman coding for avoiding the wastage of memory and decreases the symbol search time in the previous study. To further speed up the process of search for a symbol in a Huffman tree, a tree-clustering algorithm for decoding, which is independent of number of nodes and height of tree, has been used with slight modification for custom coding. It requires very few computations, since it reduces the height of the tree there by increasing the number of code words/partition. This reduced height minimizes the difference of codeword length with in the partition in order to minimize the number of redundancy codeword insertion while transforming Huffman tree to Canonical Huffman tree. Hence the time required to compute the canonical order becomes O (n) and total decoding time complexity becomes O (n+m).

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