130x1g2 - CCSDS

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RATE 1/4RATE 1/3BERCAPACITYTM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALEcodes and the corresponding estimates of BER on the error floor. Other details on algorithmsfor computing CCSDS Turbo code minimum distance and error floors can be found inreference [32].Figure 7-14 provides an illustration of the transition of a Turbo code performance curve froma steep ‘waterfall’ region into a much flatter ‘error floor’ region for two Turbo codesanalyzed as an example. This figure shows the actual simulated Turbo code performancecompared with bounds approximating the error floor.The original Turbo codes of Berrou, et al. (reference [17]) had error floors starting at a BERof about 10 -5 . By using theoretical predictors as guides, it was possible to design the Turbocodes in the Recommended Standard (reference [3]) so as to lower the error floor to possiblyinsignificant levels (e.g., as low as 10 -9 BER).LOW SNR REGIONk=BLOCK SIZECUTOFFRATETHRESHOLDHIGH SNR REGION100K=3, k=100010 -1SIMULATION10 -2RATE= 1/3CODE10 -310 -410 -5K=5, k=4096RATE=1/4CODEANALYTICALUPPER BOUND10 -610 -710 -8LOW INPUT WEIGHTS,ERROR FLOORALL INPUT WEIGTHS10 -9-101 2E b /N o (dB)34Figure 7-14: Illustration of Turbo Code Error FloorCCSDS 130.1-G-2 Page 7-14 November 2012
TM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALE8 LDPC CODES8.1 GENERALThe mid-1990s were highlighted by the rediscovery of Low Density Parity Check (LDPC)codes in the field of channel coding (reference [33]). Originally invented by R. Gallager inhis PhD thesis in 1961 (reference [34]), this coding technique was largely forgotten for morethan 30 years. The primary advance in LDPC coding is the discovery of an iterativedecoding algorithm, now called Belief Propagation (BP), which offers near-optimumperformance for large linear LDPC codes at a manageable complexity. LDPC codeperformance gains were difficult to realize technologically in the early 1960s. Severaldecades of VLSI development has finally made the implementation of these codes practical.The original construction, now called Gallager codes, has come to be regarded as a specialclass of LDPC codes. Recent advances in LDPC code construction have resulted in thedevelopment of new codes with improved performance over Gallager codes. One class ofthese codes, irregular LDPC codes (reference [35]), demonstrates improved performance inthe waterfall region. Disadvantages of irregular codes, however, include an increase, ingeneral, in the number of iterations required for decoding convergence and an unequal errorprotection between code bits resulting from the irregular structure. Another class of LDPCcodes developed using algebraic construction based on finite geometries (reference [36]) hasbeen shown to provide very low error floors and very fast iterative convergence.The following two sets of LDPC codes have been proposed, because the former is optimizedfor high rates (Near Earth) and the latter for very low SNR (Deep Space):1. In the Near Earth case, data is transmitted at many hundreds of Mb/s in a band restricted to375 MHz. A high rate code is needed to limit bandwidth expansion. Complexity must belimited to allow high data rate encoding and decoding. The number of decoding iterationsmust be low to allow the high data rate; hence convergence must be fast. For these reasons,the selected code is a quasi-cyclic high-rate LDPC code that is a modification of a regular(4,32) code, known as C2 (reference [37]).2. In the Deep Space case, data rates are relatively low, which allows low rate codes to fit inthe allocated band even though the bandwidth expansion is greater. Deep Space signals travelmuch greater distances, requiring extremely good SNR performance. This is accomplishedby using codes that have greater redundancy (low rate) and greater complexity (so they mayrequire more iterations to achieve best performance). Since the data rates are lower, thefeatures required for better performance are not a burden on the system. For these reasons, aset of nine LDPC codes belonging to the AR4JA (Accumulate, Repeat-by-4, and JaggedAccumulate) family (references [45] and [46]) have been selected.The selected code rates are 1/2, 2/3, 4/5, and approximately 7/8, which are about uniformlyspaced by 1 dB on the rate-dependent capacity curve for the binary-input AWGN channel(reference [16]). Near rate 1/2, a one-percent improvement in bandwidth efficiency costsabout 0.02 dB in power efficiency; near rate 7/8, a one-percent improvement in bandwidthefficiency costs 0.1 dB in power efficiency.CCSDS 130.1-G-2 Page 8-1 November 2012
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