Error control techniques for satellite and space communications

Two aspects of the work for NASA are examined: the construction of multi-dimensional phase modulation trellis codes and a performance analysis of these codes. A complete list is contained of all the best trellis codes for use with phase modulation. LxMPSK signal constellations are included for M = 4, 8, and 16 and L = 1, 2, 3, and 4. Spectral efficiencies range from 1 bit/channel symbol (equivalent to rate 1/2 coded QPSK) to 3.75 bits/channel symbol (equivalent to 15/16 coded 16-PSK). The parity check polynomials, rotational invariance properties, free distance, path multiplicities, and coding gains are given for all codes. These codes are considered to be the best candidates for implementation of a high speed decoder for satellite transmission. The design of a hardware decoder for one of these codes, viz., the 16-state 3x8-PSK code with free distance 4.0 and coding gain 3.75 dB is discussed. An exhaustive simulation study of the multi-dimensional phase modulation trellis codes is contained. This study was motivated by the fact that coding gains quoted for almost all codes found in literature are in fact only asymptotic coding gains, i.e., the coding gain at very high signal to noise ratios (SNRs) or very low BER. These asymptotic coding gains can be obtained directly from a knowledge of the free distance of the code. On the other hand, real coding gains at BERs in the range of 10(exp -2) to 10(exp -6), where these codes are most likely to operate in a concatenated system, must be done by simulation.