Coding equivalent to RS code and algorithm of its quick compiled code

A coding, decoding and coding technology, applied in the field of RS codes, which can solve the problems of slow speed and small area.

Inactive Publication Date: 2003-10-08
TSINGHUA UNIV
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Problems solved by technology

The circuit implemented by this method is simple and small in area, but the speed is slow and requires m clock cycles

Method used

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  • Coding equivalent to RS code and algorithm of its quick compiled code
  • Coding equivalent to RS code and algorithm of its quick compiled code
  • Coding equivalent to RS code and algorithm of its quick compiled code

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Embodiment Construction

[0039] If the design requires that the number of information symbols is k, the maximum number of correctable errors is t, and a primitive polynomial Poly(x) of order m is given, then primitive field element a is the root of the primitive polynomial. The design of the RS code representing a symbol with a power is as follows:

[0040] (1) Because the original element a's 0 to 2 m -2 to the power constitutes GF(2 m ) in the field of all 2 m -1 non-zero element, expressed by the power of a corresponding to the element, and assuming that the 0 element corresponds to the 2 of a m -1 power, use integer 2 m -1 means 0 elements, then 0 to 2 are established m -1 of 2 m integers to GF(2 m ) domain on 2 m One-to-one correspondence between elements.

[0041] (2)GF(2) m ) field multiplication:

[0042] GF(2 m The multiplication of two elements X and Y on the ) field is equal to the addition of the corresponding two exponents, that is, X=a x , Y=a y , Z=X·Y=a z , then z=x+y (if...

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Abstract

An encoding and decocing algorithm of code-element in RS codes is expressed by using the exponent of the primitive field element a. the code words of the RS codes are all in the GF (2m) field. The all non-zero elements in GF (2m) field are the integral exponents of the primitive field element a. For any nno-zero element X, if X=ax, then X is expressed by x. In encoding and decoding process, the multiplication of any two elements to X and Y in the GF (2m) field is equivalent to the addition of the corresponding two exponents, the division between X and Y is equivalent to the substration between the corresponding two conponents. The table look up method is used to treat the addition and substration between X and Y. the method provides same error correction performance with the present algorithm and avoids complicate multiply operation as well as realize encoding and decoding the RS codes at high speed and high efficiently.

Description

technical field [0001] A coding equivalent to RS code and its fast coding algorithm belong to the technical field of RS code. Background technique [0002] In a communication system, before information is sent, it is necessary to artificially add redundancy in the data stream according to certain rules so that the receiving end can perform bit error detection and correction. RS error correction coding is one of the most effective and widely used error control coding methods at present. RS codes can be used to correct random errors, and are also suitable for correcting burst errors, and have been widely used in satellite communication, digital TV transmission and other fields. [0003] Commonly used (n, k, d) represents the RS code; where n is the codeword length, k is the number of information symbols, and d is the design distance. If the maximum number of correctable errors is represented by t, then 2t is the number of check symbols. The parameters of the RS code have the...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H03M13/00
Inventor 赵明张秀军姚熠飞周世东王京姚彦
Owner TSINGHUA UNIV
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