Xilinx System Generator v2.1 Reference Guide

type of errors that can be corrected depends on the characteristics of the Reed- Solomon code.

Reed-Solomon codes are a subset of BCH (Bose, Chaudhuri, and Hocquenghem) codes and are linear block codes. A Reed-Solomon code is specified as RS(n,k) with s- bit symbols. Reed-Solomon codes are usually referred to as (n,k) codes, where n is the total number of symbols in a code block and k is the number of information or data symbols. Normally, n = 2(sw)-1, where sw is symbol width. If n is less than this, the code is referred to as a shortened code. The RS Encoder core handles both full length and shortened codes.

The RS Encoder block generates systematic code blocks. This means that the encoder takes k data symbols of s bits each and adds parity symbols to make an n symbol codeword. There are (n-k) parity symbols of s bits each. The following diagram shows a typical Reed-Solomon codeword. This is known as a Systematic code because the data is left unchanged and the parity symbols are appended.

Figure 3-42: Example of a Reed Solomon codeword

A Reed-Solomon code is characterized by two polynomials: the field polynomial and the generator polynomial. The field polynomial defines the Galois field, of which the symbols are members. The generator polynomial defines how the check symbols are generated. Both of these polynomials are usually defined in the specification for any particular Reed-Solomon code. The Reed-Solomon codeword is generated using the generator polynomial. All valid codewords are exactly divisible by the generator polynomial.

The general form of the generator polynomial is:

g( x) = ( x –ai)( x –ai+ 1 ) . . . . ( x –ai+ 2t )

and the codeword is constructed using:

c( x) = g( x) ⋅ i( x)

where

g(x) is the generator polynomial

i(x) is the information block

c(x) is a valid codeword

x is referred to as the field polynomial.

For example: Generator for RS(204,188) is:

g( x) = ( x –a0)( x –a1)( x –a2) . . . . ( x –a15)

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V2.1 specifications

Xilinx V2.1 is a notable iteration in the series of versatile and robust Field-Programmable Gate Arrays (FPGAs) developed to cater to a wide range of applications. Launched to provide enhancements in performance and flexibility, V2.1 embodies sophisticated technologies and features that stand out in the electronics industry.

One of the primary features of Xilinx V2.1 is its improved processing power. The architecture has been optimized to support higher clock speeds and increased logic density, allowing for more complex designs to be implemented effectively. This boost in performance is facilitated by utilizing advanced silicon technologies, which significantly reduce power consumption while maximizing efficiency.

Another significant characteristic of Xilinx V2.1 is its enhanced I/O (Input/Output) capabilities. The device supports a variety of industry-standard interfaces, which include PCI Express, SATA, and various serial communication protocols. Such adaptability ensures seamless integration into existing systems, providing engineers with the flexibility to adapt to various application requirements without the need for substantial redesign efforts.

Xilinx V2.1 also features improved scalability, making it a prime choice for applications that demand diverse performance levels. This device supports an array of configurations and can be used in small-scale projects as well as in larger, more demanding environments requiring extensive resources. This scalability is further aided by support for multiple development platforms, enabling rapid prototyping and simplifying the design process.

Security is increasingly becoming a priority in digital design, and Xilinx V2.1 addresses this concern via hardware security features. It includes enhanced encryption protocols and secure boot functionalities, which help protect intellectual property and sensitive data from unauthorized access.

Additionally, the integration of advanced DSP (Digital Signal Processing) blocks allows Xilinx V2.1 to efficiently handle data-intensive tasks such as video processing and real-time signal analysis. These capabilities make it suitable for applications in telecommunications, automotive systems, and industrial automation.

Xilinx V2.1 also benefits from a rich development environment, including robust software tools that facilitate design entry, simulation, and verification. The support for industry-standard programming languages like VHDL and Verilog simplifies the development process, enabling engineers to design complex systems more efficiently.

In summary, Xilinx V2.1 stands out due to its impressive combination of high performance, flexibility, scalability, security, and comprehensive development support. These features make it a valuable asset for engineers and developers looking to innovate across various sectors, from telecommunications and automotive to industrial applications.
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