130x1g2 - CCSDS

TM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALEFigure 5-1: Block Diagram of an (n,k) Reed-Solomon EncoderAttention is called to the specific recommended RS code with J = 8, E = 16, i.e., the (255,223)code. The basic codeword structure of this specific code with J = 8, E = 16, is given infigure 5-2. If desired, a ‘quick look’ at the data (information bits) would still be possiblesince the code is systematic. It should be noted that the overhead associated with the paritysymbols is only around 15 percent. This percentage increases if the code is shortened.Figure 5-2: RS Codeword Structure, J=8, E=16There are two polynomials that define each of the recommended Reed-Solomon codes in 4.2(4) and (5) of reference [3] (also see reference [16]): a code generator polynomial overGF(2 8 ) and a field generator polynomial over GF(2). The field generator polynomialF(x) = x 8 +x 7 +x 2 +x+1 is the same for both codes. The code generator polynomial g(x) hasdegree 2E = 32 for the (255,223) code and degree 2E = 16 for the (255,239) code. Theparticular polynomials that define the recommended codes were chosen to minimize theencoder hardware. The code generator polynomials are palindromes (self-reciprocalpolynomials) so that only half as many multipliers are required in the encoder circuits. Theparticular primitive element ‘α’ (and hence the field generator polynomial) was chosen tomake these multipliers as simple as possible. An encoder using the ‘dual basis’representation requires for implementation only a small number of integrated circuits or asingle VLSI chip.Figure 5-3 illustrates the construction of shortened RS codewords using virtual fill.CCSDS 130.1-G-2 Page 5-3 November 2012