Low-Density Parity-Check Code Design Techniques to Simplify Encoding

The NASA proposal for the Consultative Committee for Space Data Systems (CCSDS) experimental specification CCSDS 131.1-O-2 [1] describes a set of low-density parity-check (LDPC) codes for nearEarth and deep-space applications. That experimental specification describes two kinds of codes. The second one is a set of accumulate–repeat–4–jagged–accumulate (AR4JA) codes, which have characteristics particularly well suited to deep-space applications. One drawback of these codes is that, unlike the codes in other standards (such as Digital Video Broadcasting (DVB)-S2 [3], 802.11n [4], and 802.16e), the paritycheck matrices have not been defined to be encoding-efficient, but to improve the bit-error rate (BER) performance as much as possible. This fact allows the AR4JA codes to show better BER performance than some other standard codes. On the other hand, it makes necessary the use of dense generator matrices to encode the AR4JA codes defined in the proposal. In Figs. 1 and 2, an example parity-check matrix, H, and corresponding generator matrix, G, are displayed to show the difference between these two in terms of sparseness. The example in these figures is for a code of rate 1/2 with M = 8 and k = 64, where M is the size of the circulants that form the H matrix, and k is the information block length. The matrices shown accommodate n = 160 code symbols, but the last fifth of these are punctured (not transmitted over the channel) to yield a rate 1/2 code. We call this Code 1.