130x1g2 - CCSDS

TM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALEWithin the AR4JA family, the selected block lengths are k=1024, k=4096, and k=16384. Thethree values k={1024,4096,∞} are about uniformly spaced by 0.6 dB on the sphere-packingbound at WER=10 -8 , and reducing the last value from ∞ to 16384 makes the largest blocksize practical at a cost of about 0.3 dB. By choosing to keep k constant among familymembers, rather than n, the spacecraft’s command and data handling system can generatedata frames without knowledge of the code rate. To simplify implementation, the code ratesare exact ratios of small integers, and the choices of k are powers of two. Code C2 has rate0.87451 and size (n=8160, k=7136), which is exactly four times that of the (255,223) Reed-Solomon code.The selected codes are systematic. A low-complexity encoding method is described inreference [41]. The parity check matrices have plenty of structure to facilitate decoderimplementation (reference [42]). The AR4JA codes have irregular degree distributions,because this improves performance by about 0.5 dB at rate 1/2, compared to a regular (3,6)code (reference [44]). As the code rate increases towards unity, the performanceimprovement of an irregular degree distribution becomes small (reference [43]).8.2 APPLICATIONS OF LDPC CODESWhen designing a communications link, selection of the error correcting code requires atrade-off of several parameters. Dominant parameters typically include power efficiency,code rate (a high code rate may be required to meet a bandwidth constraint with the availablemodulations), and the block length (shorter blocks reduce latency on low data-rate links, andreduce encoder and decoder complexity). The trade-off between power efficiency andspectral efficiency for several CCSDS codes is shown in figure 8-1. The horizontal axis isthe familiar E b /N 0 , and the vertical axis shows spectral efficiency in Hz-sec/bit, the reciprocalof the potentially more familiar unit of bits/sec/Hz. It may be noted that both axes arelogarithmic. Turbo codes of block lengths k=8920 and k=1784 are shown in green, the tenLDPC codes are shown in red, and the (7,1/2) convolutional and (255,223) Reed-Solomoncodes are shown in blue, both alone and concatenated. When these codes are concatenated,performance improves with greater interleaving depth; shown are I = 1 and 5 codewords, andthe theoretical limit I = ∞. Performance is plotted at a BER of 10 -6 , and only theconvolutional (7,1/2) point moves significantly at other error rates.CCSDS 130.1-G-2 Page 8-2 November 2012