System Design For FEC In Aeronautical Telemetry

This paper contains a description of two types of forward error correction (FEC) codes for shaped offset quadrature phase shift keying, telemetry group version (SOQPSK-TG). The FEC codes are a low-density parity check (LDPC) code and a serially concatenated convolutional code (SCCC). The contributions of this paper are on the system-design level. One major contribution is to design a SCCC code word format that is as compatible as possible with the LDPC code word, which simplifies other aspects of the system design. Another major contribution is to show exactly how demodulators and decoders can be decoupled from each other at the receiver. This simplifies the demodulation process because receiver synchronization is no longer intertwined with FEC decoding. Furthermore, this enables a mix-and-match design, where demods can be chosen based on their performance and complexity tradeoffs. In fact, for the first time, we show how symbol-bysymbol demods can be used with all FEC coding/decoding options, and we also show that these demods have very attractive BER performance given their simplicity. TRANSMITTER MODEL FEC Encoders The transmitter model is shown in Figure 1. The information word (sequence) is denoted as u , {ui} i=0 , where K is the number of bits contained in the information word and each bit has a duration of Tb seconds. The FEC encoder accepts u as its input and returns the code word (sequence) c , {ci} i=0 as its output, where N is the number of symbols contained in the code word and each symbol has a duration of Ts seconds. The FEC encoder has a rate R , K/N and we have the relationship Ts = RTb. Based on analysis of link budget and throughput requirements, the iNET Communication Link Standards Working Group (CLSWG) identified a coding rate of R = 2/3 and an information word length of K = 4096 bits (code word length of N = 6144 symbols) as attractive design choices [1]. Two FEC options were identified by the CLSWG: LDPC and SCCC. Furthermore, based on its successful deployment in serial streaming telemetry (SST) links, the CLSWG identified SOQPSK-TG as the initial option for the physical-layer waveform. Figure 1 reflects the SOQPSK-based transmitter design, where the code word c is fed to the SOQPSK modulator which produces the transmitted signal s(t; c). The two FEC options and the SOQPSK-TG waveform are now specified in greater detail. The LDPC code is the R = 2/3, K = 4096 (N = 6144) code developed at NASA’s Jet Propulsion Laboratory (JPL) [2, 3]. Because the full specification of this code is found in [3], we give only cursory details here. This is a quasi-cyclic code in the family known as “Accumulate Repeat-4 Jagged Accumulate” (AR4JA) codes. The generator matrix for this code is expressed in systematic form as G = [I4096 W ], where IN denotes the N×N identity matrix. Because the generator matrix is in systematic form, the LDPC code words have the format shown in Figure 2, where the information word u occupies the first 4096 positions in c, and the parity symbols occupy the last 2048 positions in c. The full specification of the 4096× 2048 matrix W is found in [3]; suffice it to say that it is a dense matrix of 256×256 block circulants that permits a simplified hardware implementation. This code has a native rate of 4/7 and the desired rate of 2/3 is achieved by puncturing (deleting) the last 1024 columns of the original generator matrix in [3]. Thus, the sparse parity-check matrix H used in the decoding algorithm has dimensions 3072× 7168.