参数资料
| 型号： | IP-RSDEC |
| 厂商： | Altera |
| 文件页数： | 22/38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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3–2
Chapter 3: Functional Description
Background
For example, for the following information:
3
g(x) = ?? ( x – ? i + i0 )
i = 0
a is a root of the binary primitive polynomial x 8 + x 7 + x 2 + x + 1
i0 = 120
You can calculate the following parameters:
■
■
R –1=3
a = 1 ( ? is to the power 1 times i )
The field polynomial can be obtained by replacing x with 2, thus:
2 8 + 2 7 + 2 2 +2 + 1 = 391
Erasures
In normal operation, the RS decoder detects and corrects symbol errors.
The number of symbol errors that can be corrected, C , depends on the number of
check symbols, R and is given by C ? R /2.
If the location of the symbol errors is marked as an erasure, the RS decoder can correct
twice as many errors, so C ? R .
1
Erasures are symbol errors with a known location.
External circuitry identifies which symbols have errors and passes this information to
the decoder using the eras_sym signal. The eras_sym input indicates an erasure (when
the erasures-supporting decoder option is selected).
The RS decoder can work with a mixture of erasures and errors.
A codeword is correctly decoded if (2 e + E ) ? R
where:
e = errors with unknown locations
E = erasures
R = number of check symbols.
For example, with ten check symbols the decoder can correct ten erasures, or five
symbol errors, or four erasures and three symbol errors.
ability to detect errors without correction ( decfail asserted) diminishes. Refer to
Table 3–1 on page 3–4 .
Shortened Codewords
A shortened codeword contains fewer symbols than the maximum value of N , which
is 2 m –1. A shortened codeword is mathematically equivalent to a maximum-length
code with the extra data symbols at the start of the codeword set to 0.
For example, (204,188) is a shortened codeword of (255,239). Both of these codewords
use the same number of check symbols, 16.
Reed-Solomon Compiler
User Guide
November 2013 Altera Corporation
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