RSDEC-DBLK-XM-U3 Lattice, RSDEC-DBLK-XM-U3 Datasheet - Page 11

• Manufacturer Part Number: RSDEC-DBLK-XM-U3
• Description: Encoders, Decoders, Multiplexers & Demultiplexers Dynamic Block Reed Solomon Decoder
• Manufacturer: Lattice

Specifications of RSDEC-DBLK-XM-U3

• Factory Pack Quantity: 1

Lattice Semiconductor
IPUG52_01.6, December 2010
errors is determined, the decoder decides if they are within the range of correction. After determining this, the
decoder corrects the errors in the received data. A typical application of space signal processing is shown in
Figure
Figure 2-2. Application of Reed-Solomon Code in a Space Communication System
Reed-Solomon codes are defined on a finite field known as Galois field. The size of the field is determined by the
symbol width, wsymb, and is equal to 2wsymb. When n is less than its maximum value of 2wsymb-1, the corre-
sponding code RS(n,k) is referred to as a shortened code.
Reed-Solomon codes are characterized by two polynomials: the generator polynomial and the field polynomial.
The field polynomial defines the Galois field where the information and check symbols belong. The generator poly-
nomial determines the check symbol generation and it is a prime polynomial for all codewords (i.e. all codewords
are exactly divisible by the generator polynomial). Both the field and the generator polynomials are user configu-
rable.
Field Polynomial
The field polynomial is defined by its decimal value (f). The decimal value of a field polynomial is obtained by set-
ting x = 2 in the polynomial. For example, the polynomial x
nomial can be specified as any prime polynomial with decimal value up to 2
Generator Polynomial
The generator polynomial determines the value of the check symbols. The generator polynomial can be defined by
the parameters starting root (gstart) and root spacing (rootspace). The general form of the generator polyno-
mial is given by:
where  is called the primitive element of the field polynomial. For a binary Galois field GF(2),  is equal to 2.
Shortened Codes
When the size of the Reed-Solomon codewords, n, is less than the maximum possible size, 2
shortened codes. For example, RS (204,188) when wsymb = 8 is a shortened code.
Systematic Decoder
The decoder can only decode data encoded by a systematic Reed-Solomon Encoder. In a systematic encoder, the
information symbols are unchanged and are followed by check symbols in the output.
Decoding Modes
The decoder can support Error, Erasure and Puncturing modes. In the error mode no information is available about
the symbols in error. In this mode the decoder needs to compute both position and magnitude of the error symbols.
In the erasure mode the user can dynamically indicate the erased symbols using the input port ers. Erased sym-
bols are those symbols in error whose positions are known in advance. Error mode can be thought of a special
case of Erasure mode, when number of erased symbols is zero. Therefore it is not necessary to identify all correct-
able errors as erasures through the input port ers in the erasure mode and combinations of errors and erasures
2-2.
Decoded Data
Input Data
RS Encoder
RS Decoder
g(x)
=
n-k-1
i = 0

Deinterleaver
(x - 
Interleaver
rootspace
11 Dynamic Block Reed-Solomon Decoder User’s Guide
2
+ x + 1 in decimal value is 2

(gstart + i)
Convolutional
Encoder
Decoder
)
Viterbi
wsymb+1
- 1.
Functional Description
2
+ 2 + 1 = 7. The field poly-
Transmitted Data
Received Data
wsymb-1
, they are called
(1)