LZ77 基本概述-繁依Fanyi

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文章目录

LZ77 编码简介

  • LZ 编码由以色列研究者 Jacob Ziv 和 Abraham Lempel 提出，是无损压缩的核心思想。LZ 是一个系列的算法，而其中最基本的就是两人在 1977年所发表的论文《A Universal Algorithm for Sequential Compression》 中提出的 LZ77 算法。
  • LZ77 压缩是一种基于字典及滑动窗口的无损压缩技术，广泛应用于通信传输。
  • LZ77 算法不同于 Huffman 编码等基于统计的数据压缩编码，需要得到先验知识——信源的字符频率，然后进行压缩。
  • LZ77的核心思想：利用数据的重复结构信息来进行数据压缩。

LZ77 的基本原理

  • LZ77 以经常出现的字母组合（或较长的字符串）构建字典中的数据项，并且使用较短的数字（或符号）编码来代替比较复杂的数据项。数据压缩时，将从待压缩数据中读入的源数据与字典中的数据项进行匹配，从中检索出相应的代码并输出。从而实现数据的压缩
  • 在 LZ77 方法中，词典就是先前已编码序列的一部分。编码器通过一个滑动窗口来查看输入序列，如下图所示。

在这里插入图片描述

  • 这个滑动窗口包括两个部分：查找缓冲区(Search Buffer) 和 先行缓冲区(Look Ahead Buffer)
    • 查找缓冲区：包含了最近已编码序列的一部分
    • 先行缓冲区：包含待编码序列的下一部分
      这里查找缓冲区包含了 8 个符号，先行缓冲区包含 7 个符号。但在实际情况中，缓冲区要大很多。

三元组参数解释：

  • ① 匹配指针 先在 查找缓冲区 中找到移动指针，知道找到与先行缓冲区第一个字符a相匹配字符a。此时该指针与先行缓冲区的距离称为 偏移量(off) 。这里的 偏移量off 就是7。
  • ② 编码器之后查看指针位置之后的符号，查看其是否与先行缓冲区的符号相匹配。从第一个符号（匹配指针以开始所指向的位置）开始，与先行缓冲区的符号匹配，匹配到的连续符号的长度称为 匹配长度(len)。例如这里，从匹配指针所指的位置开始的符号串 abra 与 先行缓冲区中的符号串 abra 相匹配，下一位查找缓冲区的 x 与 先行缓冲区 a 不匹配，所以这里的 匹配长度len 是 4.。
  • ③ 编码器在查找缓冲区中搜素最长匹配串。找到最长的匹配串后，编码器即可用三元组 对其进行编码。这里 off 是偏移量 ，len 是匹配长度，c 是先行缓冲区中跟在该匹配项串之后的符号的码字。例如这里 匹配串 是 abra，则先行缓冲区匹配串后的码字是 r。

LZ77 算法

  • LZ77 算法执行流程如下：
    步骤 1：从输入的待压缩数据的起始位置，读取未编码的源数据，从滑动窗口的字典数据项中查找最长的匹配字符串。若结果为 T，则执行步骤 2，若结果为 F，则执行步骤 3；
    步骤 2：输出函数 F（off，len，c）。然后将窗口向后滑动到 len++，继续步骤 1；
    步骤 3：输出函数 F（0，0，c），其中 c 为下一个字符。并且窗口向后滑动（len + 1）个字符，执行步骤 1。

  • 下面是代码实现：

    /* PROG1.C                                                    */
/* Simple Hashing LZ77 Sliding Dictionary Compression Program */
/* By Rich Geldreich, Jr. October, 1993                       */
/* Originally compiled with QuickC v2.5 in the small model.   */
#include 
#include 
#include 
#include 

/* set this to 1 for a greedy encoder */
#define GREEDY    0

/* ratio vs. speed constant */
/* the larger this constant, the better the compression */
#define MAXCOMPARES 75

/* unused entry flag */
#define NIL       0xFFFF

/* bits per symbol- normally 8 for general purpose compression */
#define CHARBITS  8

/* minimum match length & maximum match length */
#define THRESHOLD 2
#define MATCHBITS 4
#define MAXMATCH  ((1 << MATCHBITS) + THRESHOLD - 1)

/* sliding dictionary size and hash table's size */
/* some combinations of HASHBITS and THRESHOLD values will not work
         correctly because of the way this program hashes strings */
#define DICTBITS  13
#define HASHBITS  10
#define DICTSIZE  (1 << DICTBITS)
#define HASHSIZE  (1 << HASHBITS)

/* # bits to shift after each XOR hash */
/* this constant must be high enough so that only THRESHOLD + 1
         characters are in the hash accumulator at one time */
#define SHIFTBITS ((HASHBITS + THRESHOLD) / (THRESHOLD + 1))

/* sector size constants */
#define SECTORBIT 10
#define SECTORLEN (1 << SECTORBIT)
#define SECTORAND ((0xFFFF << SECTORBIT) & 0xFFFF)

/* dictionary plus MAXMATCH extra chars for string comparisions */
unsigned char
        dict[DICTSIZE + MAXMATCH];

/* hashtable & link list table */
unsigned int
        hash[HASHSIZE],
        nextlink[DICTSIZE];

/* misc. global variables */
unsigned int
        matchlength,
        matchpos,
        bitbuf,
        bitsin,
        masks[17] = {0,1,3,7,15,31,63,127,255,511,1023,2047,4095,8191,16383,32767,65535};

FILE *infile, *outfile;

/* writes multiple bit codes to the output stream */
void SendBits(unsigned int bits, unsigned int numbits)
{

        bitbuf |= (bits << bitsin);

        bitsin += numbits;

        if (bitsin > 16)         /* special case when # bits in buffer exceeds 16 */
        {
                if (putc(bitbuf & 0xFF, outfile) == EOF)
                {
                        printf("nerror writing to output file");
                        exit(EXIT_FAILURE);
                }
                bitbuf = bits >> (8 - (bitsin - numbits));
                bitsin -= 8;
        }

        while (bitsin >= 8)
        {
                if (putc(bitbuf & 0xFF, outfile) == EOF)
                {
                        printf("nerror writing to output file");
                        exit(EXIT_FAILURE);
                }
                bitbuf >>= 8;
                bitsin -= 8;
        }

}

/* reads multiple bit codes from the input stream */
unsigned int ReadBits(unsigned int numbits)
{

        register unsigned int i;

        i = bitbuf >> (8 - bitsin);

        while (numbits > bitsin)
        {
                if ((bitbuf = getc(infile)) == EOF)
                {
                        printf("nerror reading from input file");
                        exit(EXIT_FAILURE);
                }
                i |= (bitbuf << bitsin);
                bitsin += 8;
        }

        bitsin -= numbits;

        return (i & masks[numbits]);

}

/* sends a match to the output stream */
void SendMatch(unsigned int matchlen, unsigned int matchdistance)
{
        SendBits(1, 1);

        SendBits(matchlen - (THRESHOLD + 1), MATCHBITS);

        SendBits(matchdistance, DICTBITS);
}

/* sends one character (or literal) to the output stream */
void SendChar(unsigned int character)
{
        SendBits(0, 1);

        SendBits(character, CHARBITS);
}

/* initializes the search structures needed for compression */
void InitEncode(void)
{
        register unsigned int i;

        for (i = 0; i < HASHSIZE; i++) hash[i] = NIL;

        nextlink[DICTSIZE] = NIL;

}

/* loads dictionary with characters from the input stream */
unsigned int LoadDict(unsigned int dictpos)
{
        register unsigned int i, j;

        if ((i = fread(&dict[dictpos], sizeof (char), SECTORLEN, infile)) == EOF)
        {
                printf("nerror reading from input file");
                exit(EXIT_FAILURE);
        }

        /* since the dictionary is a ring buffer, copy the characters at
                 the very start of the dictionary to the end */
        if (dictpos == 0)
        {
                for (j = 0; j < MAXMATCH; j++) dict[j + DICTSIZE] = dict[j];
        }

        return i;
}

/* deletes data from the dictionary search structures */
/* this is only done when the number of bytes to be
         compressed exceeds the dictionary's size */
void DeleteData(unsigned int dictpos)
{

        register unsigned int i, j;

        j = dictpos;        /* put dictpos in register for more speed */

        /* delete all references to the sector being deleted */

        for (i = 0; i < DICTSIZE; i++)
                if ((nextlink[i] & SECTORAND) == j) nextlink[i] = NIL;

        for (i = 0; i < HASHSIZE; i++)
                if ((hash[i] & SECTORAND) == j) hash[i] = NIL;

}

/* hash data just entered into dictionary */
/* XOR hashing is used here, but practically any hash function will work */
void HashData(unsigned int dictpos, unsigned int bytestodo)
{
        register unsigned int i, j, k;

        if (bytestodo <= THRESHOLD)   /* not enough bytes in sector for match? */
                for (i = 0; i < bytestodo; i++) nextlink[dictpos + i] = NIL;
        else
        {
                /* matches can't cross sector boundries */
                for (i = bytestodo - THRESHOLD; i < bytestodo; i++)
                        nextlink[dictpos + i] = NIL;

                j = (((unsigned int)dict[dictpos]) << SHIFTBITS) ^ dict[dictpos + 1];

                k = dictpos + bytestodo - THRESHOLD;  /* calculate end of sector */

                for (i = dictpos; i < k; i++)
                {
                        nextlink[i] = hash[j = (((j << SHIFTBITS) & (HASHSIZE - 1)) ^ dict[i + THRESHOLD])];
                        hash[j] = i;
                }
        }
}

/* finds match for string at position dictpos */
/* this search code finds the longest AND closest
         match for the string at dictpos */
void FindMatch(unsigned int dictpos, unsigned int startlen)
{
        register unsigned int i, j, k;
        unsigned char l;

        i = dictpos; matchlength = startlen; k = MAXCOMPARES;
        l = dict[dictpos + matchlength];

        do
        {
                if ((i = nextlink[i]) == NIL) return;   /* get next string in list */

                if (dict[i + matchlength] == l)        /* possible larger match? */
                {
                        for (j = 0; j < MAXMATCH; j++)          /* compare strings */
                                if (dict[dictpos + j] != dict[i + j]) break;

                        if (j > matchlength)  /* found larger match? */
                        {
                                matchlength = j;
                                matchpos = i;
                                if (matchlength == MAXMATCH) return;  /* exit if largest possible match */
                                l = dict[dictpos + matchlength];
                        }
                }
        }
        while (--k);  /* keep on trying until we run out of chances */

}

/* finds dictionary matches for characters in current sector */
void DictSearch(unsigned int dictpos, unsigned int bytestodo)
{

        register unsigned int i, j;

#if (GREEDY == 0)

        unsigned int matchlen1, matchpos1;

        /* non-greedy search loop (slow) */

        i = dictpos; j = bytestodo;

        while (j) /* loop while there are still characters left to be compressed */
        {
                FindMatch(i, THRESHOLD);

                if (matchlength > THRESHOLD)
                {
                        matchlen1 = matchlength;
                        matchpos1 = matchpos;

                        for ( ; ; )
                        {
                                FindMatch(i + 1, matchlen1);

                                if (matchlength > matchlen1)
                                {
                                        matchlen1 = matchlength;
                                        matchpos1 = matchpos;
                                        SendChar(dict[i++]);
                                        j--;
                                }
                                else
                                {
                                        if (matchlen1 > j)
                                        {
                                                matchlen1 = j;
                                                if (matchlen1 <= THRESHOLD) { SendChar(dict[i++]); j--; break; }
                                        }

                                        SendMatch(matchlen1, (i - matchpos1) & (DICTSIZE - 1));
                                        i += matchlen1;
                                        j -= matchlen1;
                                        break;
                                }
                        }
                }
                else
                {
                        SendChar(dict[i++]);
                        j--;
                }
        }

#else

        /* greedy search loop (fast) */

        i = dictpos; j = bytestodo;

        while (j) /* loop while there are still characters left to be compressed */
        {
                FindMatch(i, THRESHOLD);

                if (matchlength > j) matchlength = j;     /* clamp matchlength */

                if (matchlength > THRESHOLD)  /* valid match? */
                {
                        SendMatch(matchlength, (i - matchpos) & (DICTSIZE - 1));
                        i += matchlength;
                        j -= matchlength;
                }
                else
                {
                        SendChar(dict[i++]);
                        j--;
                }
        }

#endif

}

/* main encoder */
void Encode (void)
{
        unsigned int dictpos, deleteflag, sectorlen;
        unsigned long bytescompressed;

        InitEncode();

        dictpos = deleteflag = 0;

        bytescompressed = 0;

        while (1)
        {
                /* delete old data from dictionary */
                if (deleteflag) DeleteData(dictpos);

                /* grab more data to compress */
                if ((sectorlen = LoadDict(dictpos)) == 0) break;

                /* hash the data */
                HashData(dictpos, sectorlen);

                /* find dictionary matches */
                DictSearch(dictpos, sectorlen);

                bytescompressed += sectorlen;

                printf("r%ld", bytescompressed);

                dictpos += SECTORLEN;

                /* wrap back to beginning of dictionary when its full */
                if (dictpos == DICTSIZE)
                {
                        dictpos = 0;
                        deleteflag = 1;   /* ok to delete now */
                }
        }

        /* Send EOF flag */
        SendMatch(MAXMATCH + 1, 0);

        /* Flush bit buffer */
        if (bitsin) SendBits(0, 8 - bitsin);

        return;
}

/* main decoder */
void Decode (void)
{

        register unsigned int i, j, k;
        unsigned long bytesdecompressed;

        i = 0;
        bytesdecompressed = 0;

        for ( ; ; )
        {
                if (ReadBits(1) == 0)   /* character or match? */
                {
                        dict[i++] = ReadBits(CHARBITS);
                        if (i == DICTSIZE)
                        {
                                if (fwrite(&dict, sizeof (char), DICTSIZE, outfile) == EOF)
                                {
                                        printf("nerror writing to output file");
                                        exit(EXIT_FAILURE);
                                }
                                i = 0;
                                bytesdecompressed += DICTSIZE;
                                printf("r%ld", bytesdecompressed);
                        }
                }
                else
                {
                        /* get match length from input stream */
                        k = (THRESHOLD + 1) + ReadBits(MATCHBITS);

                        if (k == (MAXMATCH + 1))      /* Check for EOF flag */
                        {
                                if (fwrite(&dict, sizeof (char), i, outfile) == EOF)
                                {
                                        printf("nerror writing to output file");
                                        exit(EXIT_FAILURE);
                                }
                                bytesdecompressed += i;
                                printf("r%ld", bytesdecompressed);
                                return;
                        }

                        /* get match position from input stream */
                        j = ((i - ReadBits(DICTBITS)) & (DICTSIZE - 1));

                        if ((i + k) >= DICTSIZE)
                        {
                                do
                                {
                                        dict[i++] = dict[j++];
                                        j &= (DICTSIZE - 1);
                                        if (i == DICTSIZE)
                                        {
                                                if (fwrite(&dict, sizeof (char), DICTSIZE, outfile) == EOF)
                                                {
                                                        printf("nerror writing to output file");
                                                        exit(EXIT_FAILURE);
                                                }
                                                i = 0;
                                                bytesdecompressed += DICTSIZE;
                                                printf("r%ld", bytesdecompressed);
                                        }
                                }
                                while (--k);
                        }
                        else
                        {
                                if ((j + k) >= DICTSIZE)
                                {
                                        do
                                        {
                                                dict[i++] = dict[j++];
                                                j &= (DICTSIZE - 1);
                                        }
                                        while (--k);
                                }
                                else
                                {
                                        do
                                        {
                                                dict[i++] = dict[j++];
                                        }
                                        while (--k);
                                }
                        }
                }
        }

}

int main(int argc, char *argv[])
{
        char *s;

        if (argc != 4)
        {
                printf("n'prog1 e file1 file2' encodes file1 into file2.n"
                                                 "'prog1 d file2 file1' decodes file2 into file1.n");
                return EXIT_FAILURE;
        }
        if ((s = argv[1], s[1] || strpbrk(s, "DEde") == NULL)
         || (s = argv[2], (infile  = fopen(s, "rb")) == NULL)
         || (s = argv[3], (outfile = fopen(s, "wb")) == NULL)) {
                printf("??? %sn", s);  return EXIT_FAILURE;
        }

        /* allocate 4k I/O buffers for a little speed */
        setvbuf( infile, NULL, _IOFBF, 4096);
        setvbuf( outfile, NULL, _IOFBF, 4096);

        if (toupper(*argv[1]) == 'E')
        {
                printf("Compressing %s to %sn", argv[2], argv[3]);
                Encode();
        }
        else
        {
                printf("Decompressing %s to %sn", argv[2], argv[3]);
                Decode();
        }

        fclose(infile);  fclose(outfile);

        return EXIT_SUCCESS;
}

参考文献

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