RS码的英文论文和翻译.doc

Binary-Input RS EncoderThe Binary-Input RS Encoder block creates a Reed-Solomon code with message length K and codeword length N. You specify both N and K directly in the dialog box. The symbols for the code are binary sequences of length M, corresponding to elements of the Galois field GF(2M), where the first bit in each sequence is the most significant bit. Restrictions on M and N are given in the section Restrictions on the M and the Codeword Length N below. The difference N-K must be an even integer. The input and output are binary-valued signals that represent messages and codewords, respectively. The input must be a frame-based column vector whose length is an integer multiple of M*K. For more information on representing data for Reed-Solomon codes, see the section Integer Format (Reed-Solomon only). The default value of M is the smallest integer that is greater than or equal to log2(N+1), that is, ceil(log2(N+1). If N is less than 2M-1, the block uses a shortened Reed-Solomon code. Each M*K input bits represent K integers between 0 and 2M-1. Similarly, each M*N output bits represent N integers between 0 and 2M-1. These integers in turn represent elements of the Galois field GF(2M). An (N,K) Reed-Solomon code can correct up to floor(N-K)/2) symbol errors (not bit errors) in each codeword.Specifying the Primitive PolynomialYou can specify the primitive polynomial that defines the finite field GF(2M), corresponding to the integers that form messages and codewords. To do so, first select the box next to Specify primitive polynomial. Then, in the Primitive polynomial field, enter a binary row vector that represents a primitive polynomial over GF(2) of degree M, in descending order of powers. For example, to specify the polynomial ,enter the vector 1 0 1 1. If you do not select the box next to Specify primitive polynomial, the block uses the default primitive polynomial of degree M = ceil(log2(N+1). You can display the default polynomial by entering primpoly(ceil(log2(N+1) at the MATLAB prompt.Restrictions on the M and the Codeword Length NThe restrictions on the degree M of the primitive polynomial and the codeword length N are as follows: If you do not select the box next to Specify primitive polynomial, N must lie in the rangemust lie in the range . If you do select the box next to Specify primitive polynomial, N must lie in the range and M must lie in the range .Specifying the Generator PolynomialYou can specify the generator polynomial for the Reed-Solomon code. To do so, first select the box next to Specify generator polynomial. Then, in the Generator polynomial field, enter an integer row vector whose entries are between 0 and 2M-1. The vector represents a polynomial, in descending order of powers, whose coefficients are elements of GF(2M) represented in integer format. See the section Integer Format (Reed-Solomon only) for more information about integer format. The generator polynomial must be equal to a polynomial with a factored form , where a is the primitive element of the Galois field over which the input message is defined, and b is a non-negative integer. If you do not select the box next to Specify generator polynomial, the block uses the default generator polynomial, corresponding to b=1, for Reed-Solomon encoding. You can display the default generator polynomial by typing rsgenpoly(N1,K1), where N1=2M-1 and K1=K+(N1-N), at the MATLAB prompt, if you are using the default primitive polynomial. If the Specify primitive polynomial box is selected, and you specify the primitive polynomial specified as poly, the default generator polynomial is rsgenpoly(N1,K1,poly).Binary-Output RS Decoder The Binary-Output RS Decoder block recovers a binary message vector from a binary Reed-Solomon codeword vector. For proper decoding, the parameter values in this block should match those in the corresponding Binary-Input RS Encoder block. The Reed-Solomon code has message length K and codeword length N. You specify both N and K directly in the dialog box. The symbols for the code are binary sequences of length M, corresponding to elements of the Galois field GF(2M), where the first bit in each sequence is the most significant bit. Restrictions on M and N are described in the section Restrictions on the M and the Codeword Length N. The difference N-K must be an even integer. The input and output are binary-valued signals that represent messages and codewords, respectively. The input must be a frame-based column vector whose length is an integer multiple of M*K. The output is a frame-based column vector whose length is the same integer multiple of M*N. For more information on representing data for Reed-Solomon codes, see the section Integer Format (Reed-Solomon only). The default value of M is ceil(log2(N+1), that is, the smallest integer greater than or equal to log2(N+1). You can change the value of M from the default by specifying the primitive polynomial for GF(2M), as described in the section Specifying the Primitive Polynomial below. If N is less than 2M-1, the block uses a shortened Reed-Solomon code. You can also specify the generator polynomial for the Reed-Solomon code, as described in the section Specifying the Generator Polynomial. Each M*K input bits represent K integers between 0 and 2M-1. Similarly, each M*N output bits represent N integers between 0 and 2M-1. These integers in turn represent elements of the Galois field GF(2M). The second output is a vector of the number of errors detected during decoding of the codeword. A -1 indicates that the block detected more errors than it could correct using the coding scheme. An (N,K) Reed-Solomon code can correct up to floor(N-K)/2) symbol errors (not bit errors) in each codeword. You can disable the second output by clearing the box next to Output port for number of corrected errors. This removes the blocks second output port.Integer-Input RS EncoderThe Integer-Input RS Encoder block creates a Reed-Solomon code with message length K and codeword length N. You specify both N and K directly in the block dialog. The symbols for the code are integers between 0 and 2M-1, which represent elements of the finite field GF(2M). Restrictions on M and N are described in the section Restrictions on M and the Codeword Length N below. The difference N - K must be an even integer. The input and output are integer-valued signals that represent messages and codewords, respectively. The input must be a frame-based column vector whose length is an integer multiple of K. The output is a frame-based column vector whose length is the same integer multiple of N. For more information on representing data for Reed-Solomon codes, see the section Integer Format (Reed-Solomon only). The default value of M is the smallest integer that is greater than or equal to log2(N+1), that is, ceil(log2(N+1). You can change the value of M from the default by specifying the primitive polynomial for GF(2M), as described in the section Specifying the Primitive Polynomial following. If N is less than 2M-1, the block uses a shortened Reed-Solomon code. An (N, K) Reed-Solomon code can correct up to floor(N-K)/2) symbol errors (not bit errors) in each codeword.Specifying the Primitive PolynomialYou can specify the primitive polynomial that defines the finite field GF(2M), corresponding to the integers that form messages and codewords. To do so, first check the box next to Specify primitive polynomial. Then, in the Primitive polynomial field, enter a binary row vector that represents a primitive polynomial over GF(2) of degree M, in descending order of powers. For example, to specify the polynomial, enter the vector 1 0 1 1.If you do not select the box next to Specify primitive polynomial, the block uses the default primitive polynomial of degree M = ceil(log2(N+1). You can display the default polynomial by entering primpoly(ceil(log2(N+1) at the MATLAB prompt.Restrictions on M and the Codeword Length NThe restrictions on the degree M of the primitive polynomial and the codeword length N are as follows:If you do not select the box next to Specify primitive polynomial, N must lie in the rangeIf you do select the box next to Specify primitive polynomial, N must lie in the range and M must lie in the rangeSpecifying the Generator PolynomialYou can specify the generator polynomial for the Reed-Solomon code. To do so, first select the box next to Specify generator polynomial. Then, in the Generator polynomial field, enter an integer row vector whose entries are between 0 and 2M-1. The vector represents a polynomial, in descending order of powers, whose coefficients are elements of GF(2M) represented in integer format. See the section Integer Format (Reed-Solomon only) for more information about integer format. The generator polynomial must be equal to a polynomial with a factored formwhere a is the primitive element of the Galois field over which the input message is defined, and b is an integer. If you do not select the box next to Specify generator polynomial, the block uses the default generator polynomial, corresponding to b=1, for Reed-Solomon encoding. You can display the default generator polynomial by typing rsgenpoly(N1,K1), where N1 = 2M-1 and K1 = K+(N1-N), at the MATLAB prompt, if you are using the default primitive polynomial. If the Specify primitive polynomial box is selected, and you specify the primitive polynomial specified as poly, the default generator polynomial is rsgenpoly(N1,K1,poly).Integer-Output RS DecoderThe Integer-Output RS Decoder block recovers a message vector from a Reed-Solomon codeword vector. For proper decoding, the parameter values in this block should match those in the corresponding Integer-Input RS Encoder block. The Reed-Solomon code has message length K and codeword length N. You specify both N and K directly in the block dialog. The symbols for the code are integers between 0 and 2M-1, which represent elements of the finite field GF(2M). Restrictions on M and N are described in the section Restrictions on M and the Codeword Length N following. The difference N - K must be an even integer. The input and output are integer-valued signals that represent messages and codewords, respectively. The input must be a frame-based column vector whose length is an integer multiple of K. The output is a frame-based column vector whose length is the same integer multiple of N. For more information on representing data for Reed-Solomon codes, see the section Integer Format (Reed-Solomon only). The default value of M is ceil(log2(N+1), that is, the smallest integer greater than or equal to log2(N+1). You can change the value of M from the default by specifying the primitive polynomial for GF(2M), as described in the section Specifying the Primitive Polynomial below. If N is less than 2M-1, the block uses a shortened Reed-Solomon code. You can also specify the generator polynomial for the Reed-Solomon code, as described in the section Specifying the Generator Polynomial. An (N, K) Reed-Solomon code can correct up to floor(N-K)/2) symbol errors (not bit errors) in each codeword. The second output is the number of errors detected during decoding of the codeword. A -1 indicates that the block detected more errors than it could correct using the coding scheme. An (N,K) Reed-Solomon code can correct up to floor(N-K)/2) symbol errors (not bit errors) in each codeword. You can disable the second output by clearing the box next to Output number of corrected errors. This removes the blocks second output port. The sample times of the input and output signals are equal.二进制输入RS编码二进制输入的RS编码器的结构创建一个消息长度为k和码字长度n的Reed - Solomon码。同时指定了N和K，直接在对话框中。为代码的符号二进制序列的长度为m，对应于伽罗瓦域GF（2m）上元素，其中在每一个序列的第一位也是最重要的一点。在M和N的限制给出的M和码字长度为n的一节限制。所不同的N - k必须是偶数。输入和输出是二进制值的信号，表示消息和码字，分别为。输入必须是基于帧的列向量，其长度是M*光整数倍如需有关代表的Reed - Solomon码的数据信息，请参阅整数格式（里德所罗门只）。“M的默认值是最小的整数，它是大于或等于的log2（N +1）个，即性细胞（的log2（N +1）个）。如果N大于2米- 1，则该块使用缩短Reed - Solomon码。每个M* K输入位代表之间的整数0 K表和2M- 1。同样，每一个M* N个输出位表示0和2M- 1的N个整数。反过来，这些整数代表伽罗瓦域GF（2m）上元素。一个（n，K）的Reed - Solomon码可以更正到楼（NK细胞）/ 2）在每个码字符号错误（不是位错误）。指定的本原多项式可以指定本原多项式定义有限域GF（2m）上，对应的整数，形成信息和字码。为此，首先选择旁边的框指定本原多项式。然后，在本原多项式字段中，输入一个二进制表示一个行向量本原多项式在GF（2）M在降度的权力秩序。例如，要指定多项式输入向量1 01 1。如果您没有选择旁边的框指定本原多项式，块使用了默认的m=性细胞本原多项式（的log2（N +1）个）。您可以显示输入（log2（N +1个）在MATLAB提示符默认多项式。在M的限制和码字长度为n对M和本原多项式程度的码字长度为N的限制如下：如果您没有选择旁边的框指定本原多项式，N必须位于该区域中如果你选择旁边的框指定本原多项式，N必须位于范围和M的范围必须位于。可以指定为里德所罗门码的生成多项式。为此，首先选择旁边的框指定生成多项式。然后，在生成多项式字段中，输入一个整数列向量，其作品介于0和2M- 1。矢量代表了递减的权力阶多项式，其系数是绿元素（200万）代表整数格式。如需关于整数部分整数格式的信息格式（里德所罗门只）。与生成多项式必须等于一个多项式的形式因素.其中a是它的伽罗瓦场的输入消息的定义是基本元素，而B是一个非负整数。如果您没有选择旁边的框指定的生成多项式，块使用默认的生成多项式，对应于b= 1，为里德所罗门编码。您可以通过键入rsgenpoly显示默认生成多项式（N1，K1）的，其中N1=2 M - 1的K和K1=（N1- N）的在MATLAB提示，如果您使用的是默认的本原多项式。如果指定本原多项式框被选中，并指定本原多项式为聚指定，则默认生成多项式为（N1，K1）。二进制输出的RS译码器二进制输出的RS解码器结构恢复从一个二进制里德所罗门码向量二进制消息向量。为了正确解码，在这个街区的参数值应匹配相应的二进制输入的RS编码器的结构的。在里德所罗门码的消息长度为k和码字长度n。同时指定了N和K，直接在对话框中。为代码的符号是二进制序列长度为m，对应于伽罗瓦域GF（2m）上，其中每个序列的第一位也是最重要的位元素。在M和N的限制一节所述的限制M和码字长度n。所不同的N - k必须是偶数。输入和输出是二进制值的信号，表示消息和码字，分别为。输入必须是基于帧的列向量，其长度是M*整数倍。输出是一个框架的列向量，其长度是M*全相同的整数倍。如需有关代表的Reed - Solomon码的数据信息，请参阅整数格式（里德所罗门只）。“M的默认值是（log2（N +1）个），也就是最小的整数大于或等于的log2（N +1）个。您可以通过指定的绿本原多项式（2M），如在指定的本原多项式下面一节中描述的M从默认值。如果N大于2M- 1，则该块使用缩短Reed - Solomon码。您也可以指定为里德所罗门码的生成多项式，如在指定的生成多项式的一节所述。每个M* K输入位代表之间的整数0 K表和2M- 1。同样，每一个M* N个输出位表示0和2M- 1的N个整数。反过来，这些整数代表伽罗瓦域GF（2m）上元素。第二个输出是一个码字的解码过程中检测到的错误数矢量。A-1指示块检测更多的错误可能比正确使用的编码方案。一个（n，K）的Reed - Solomon码可以更正到楼（NK）/ 2）在每个码字符号错误（不是位错误）。您可以通过清除框旁边的输出端口的纠正错误数第二个输出。这消除块的第二个输出端口。整数输入RS编码该整数输入RS编码块创建一个具有消息长度为k和码字长度n的Reed - Solomon码。同时指定了N和K块直接对话。对代码的符号是介于0和2M- 1的整数，它代表了有限域GF（2m）上元素。在M和N的限制上介绍了M和码字长度为n的一节限制。所不同的-k必须是偶数。输入和输出是整数值的信号，表示消息和码字，分别为。输入必须是基于帧的列向量，其长度为K的整数倍。输出是一个框架的列向量，其长度为n的整数倍相同。如需有关代表的Reed - Solomon码的数据信息，请参阅整数格式（里德所罗门只）。“M的默认值是最小的整数，它是大于或等于的log2（N +1）个，即（log2（N +1）个）。您可以通过指定的绿本原多项式（2M），如在指定的本原多项式以下部分描述了M由默认值。如果N大于2M-