130x1g2 - CCSDS

TM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALEsimply by considering two I×n matrices, one at the input of the channel and one at the output(see figure 5-4). For interleaving, put the I codewords, each with length n, into rows 1,2,...,Iof the matrix, then transmit the symbols of columns 1,2,...,n through the channel. For deinterleaving,do the reverse operation.Figure 5-4: Matrix Used for InterleavingFigure 5-4 illustrates the matrix used for interleaving I RS codewords (interleaving depth I).It should be noted that this matrix, by itself, does not specify in which order the inputinformation symbols should fill up the matrix cells not reserved for parity. If successiveinformation symbols are written into the matrix in the ‘natural’ ordering, row by row, so as tofill up codewords one at a time, this requires holding I–1 full codewords before any of thecolumns of the matrix can be read out. On the other hand, if successive information symbolsare written into the matrix column by column, there is no need to store the entire array ofcode symbols because each column of I newly written symbols can be immediately read outas the next I symbols of the RS codeword, as soon as the encoder computes the (linear)contribution of each of these I symbols to its corresponding set of RS parity symbols. This isequivalent to the method specified in the Recommended Standard (reference [3]). Onepotential disadvantage of the recommended method is that it spreads individual RS codeworderrors across more source blocks than the ‘natural’ ordering.Interleaving of I RS codewords produces a codeblock of length I * [RS codeword length];i.e., the entire package of I RS codewords constitutes one RS codeblock. However, it iscustomary to compute WER for individual RS codewords rather than for the wholeinterleaved codeblock. The error rate on the interleaved codeblock is the FER for CCSDSframes.5.4 HARD ALGEBRAIC DECODING OF REED-SOLOMON CODESUnlike the ‘soft’ channel symbol values that are input to a Viterbi decoder for convolutionalcodes, the symbols input to the Reed-Solomon decoder are ‘hard’, which means that the RSdecoder operates on symbols drawn from exactly the same alphabet as that used in producingthe encoded symbols. This generation of hard symbol inputs to the RS decoder happensautomatically when these symbols are generated by a Viterbi decoder for an innerconvolutional code. In this case, the Viterbi decoder generates hard bit-by-bit decisions, andCCSDS 130.1-G-2 Page 5-5 November 2012