Block Markov superposition transmission of convolutional codes with minimum shift keying signalling

In this study, the authors´ present a scheme, denoted as BMST-MSK, which combines the block Markov superposition transmission (BMST) with the minimum shift keying (MSK) signalling. The BMST-MSK can be implemented in two forms - the BMST with recursive MSK (BMST-RMSK) and the BMST with non-recursive MSK (BMST-NRMSK). The BMST-MSK admits a sliding-window decoding/demodulation algorithm, where two schedules with or without iterative processing between the BMST and MSK (referred to as outer iteration) are discussed. To analyse the asymptotic performance of BMST-MSK, the authors´ first assume a genie-aided decoder and then derive the union bound for the equivalent genie-aided system. Numerical results show that the performances of the BMST-MSK match well with the derived lower bounds in the low error rate regions. From simulations, the authors´ found that the outer iterations can provide performance improvement for the BMST-RMSK, but not for the BMST-NRMSK. Taking a (2,1,2) convolutional code with input length of 10 000 bits as the basic code, the BMST-NRMSK achieves a bit-error-rate of 10^-5 at E_b/N₀ = 0.45 dB over additive white Gaussian noise channels, which is away from the Shannon limit about 0.25 dB.