Altera Reed-Solomon Compiler Manual de usuario descargar pdf (Pagina 20)

3–2 Chapter 3: Functional Description

Background

Reed-Solomon Compiler December 2014 Altera Corporation

User Guide

For example, for the following information:

a is a root of the binary primitive polynomial x

+ x

+ 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

+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 

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 (2e + E) 

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.

1 If the number of erasures marked approaches the number of check symbols, the

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

–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.

g(x) = (x – 

i + i

)

i = 0

1 2 ... 15 16 17 18 19 20 21 22 23 24 25 ... 35 36

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