B n 2j1 255 symbols per r s codeword c 2e is the

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Unformatted text preview: d. c) 2E is the number of R-S symbols among n symbols of an R-S codeword representing parity checks. d) k = n–2E is the number of R-S symbols among n R-S symbols of an R-S codeword representing information. 4.3.3 FIELD GENERATOR POLYNOMIAL The field generator polynomial shall be: F(x) = x8 + x7 + x2 + x + 1 over GF(2). 4.3.4 CODE GENERATOR POLYNOMIAL The code generator polynomial shall be: 127 + E g(x) = ∏(x–α 11j 2E ) j=128 – E = ∑ Gix i i=0 over GF(28), where F(α) = 0. NOTES 1 It should be recognized that α11 is a primitive element in GF(28) and that F(x) and g(x) characterize a (255,223) Reed-Solomon code when E = 16 and a (255,239) ReedSolomon code when E = 8. 2 The selected code is a systematic code. This results in a systematic codeblock. CCSDS 131.0-B-2 Page 4-2 August 2011 CCSDS RECOMMENDED STANDARD FOR TM SYNCHRONIZATION AND CHANNEL CODING 4.3.5 SYMBOL INTERLEAVING The allowable values of interleaving depth are I=1, 2, 3, 4, 5, and 8. 4.3.5.1 NOTE – I=1 is equivalent to the absence of interleaving. The interleaving depth shall normally be fixed on a Physical Channel for a Mission 4.3.5.2 Phase. NOTE – 4.3.6 Discussion of symbol interleaving is contained in 4.4.1. MAXIMUM CODEBLOCK LENGTH The maximum codeblock length, in R-S symbols, shall be determined by the following equation: Lmax = nI = (2J – 1)I = 255I 4.3.7 SHORTENED CODEBLOCK LENGTH 4.3.7.1 A shortened codeblock length may be used to accommodate frame lengths smaller than the maximum. NOTE – However, since the Reed-Solomon code is a block code, the decoder must always operate on a full block basis. 4.3.7.2 To achieve a full codeblock, ‘virtual fill’ shall be added to make up the difference between the shortened block and the maximum codeblock length. NOTES 1 The characteristics and limitations of virtual fill are covered in 4.3.8.2. 2 Since the virtual fill is not transmitted, both encoder and decoder need to be set to insert it with the proper length for the encoding and decoding processes to be carried out properly. 4.3.7.3 When an encoder (initially c...
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