参数资料
| 型号： | IP-RSDEC |
| 厂商： | Altera |
| 文件页数： | 21/38页 |
| 文件大小： | 0K |
| 描述： | IP REED-SOLOMON DECODER |
| 标准包装： | 1 |
| 系列： | * |
| 类型： | MegaCore |
| 功能： | Reed-Solomon 解码器 |
| 许可证： | 初始许可证 |
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3. Functional Description
Background
To use Reed-Solomon (RS) codes, a data stream is first broken into a series of
codewords. Each codeword consists of several information symbols followed by
several check symbols (also known as parity symbols or redundant symbols).
Symbols can contain an arbitrary number of bits. In an error correction system, the
encoder adds check symbols to the data stream prior to its transmission over a
communications channel. When the data is received, the decoder checks for and
corrects any errors ( Figure 3–1 ).
Figure 3–1. RS Codeword Example
Symbol
Codewo r d
4 to 10 bits
pe r symbol.
0010
0110
1010
0011
0111
1011
I n fo r matio n symbols, which
co n tai n the o r igi n al data.
Check symbols, added by
the RS e n code r befo r e
t r a n smissio n ove r a
commu n icatio n s cha nn el.
RS codes are described as ( N , K ), where N is the total number of symbols per
codeword and K is the number of information symbols. R is the number of check
symbols ( N – K ). Errors are defined on a symbol basis. Any number of bit errors
within a symbol is considered as only one error.
RS codes are based on finite-field (i.e., Galois field) arithmetic. Any arithmetic
operation (addition, subtraction, multiplication, and division) on a field element gives
a result that is an element of the field. The size of the Galois field is determined by the
number of bits per symbol—specifically, the field has 2 m elements, where m is the
number of bits per symbol. A specific Galois field is defined by a polynomial, which is
user-defined for the RS Compiler. IP Toolbench lets you select only valid field
polynomials.
The maximum number of symbols in a codeword is limited by the size of the finite
field to 2 m – 1. For example, a code based on 10-bit symbols can have up to 1,023
symbols per codeword. The RS Compiler supports shortened codewords.
The following equation represents the generator polynomial of the code:
R – 1
g(x) = ?? ( x – ? a.i + i0 )
i = 0
where:
i0 is the first root of the generator polynomial
a is the rootspace
R is the number of check symbols
? is a root of the polynomial.
November 2013
Altera Corporation
Reed-Solomon Compiler
User Guide
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