Iterative demodulation and decoding of coded non-square QAM

It is shown that a non-square (NS) 2²ⁿ⁺¹-ary quadrature amplitude modulation (QAM) can be decomposed into a single-parity-check (SPC) block encoder and a memoryless modulator in such a way that the inherent block encoder has a recursive nature. When concatenated with a forward-error-correcting (FEC) code, iterative demodulation and decoding of the FEC code and the inherent SPC code of NS-2²ⁿ⁺¹-QAM is then possible. The capacity and bit/symbol-error-rate (BER/SER) performance of coded and uncoded NS-2²ⁿ⁺¹-QAM systems are given and compared to those of other 2²ⁿ⁺¹-ary systems. Simulation results show that, with iterative demodulation and decoding, coded NS-8QAM performs 0.5 dB better than standard 8QAM and 0.7 dB better than 8PSK at BER = 10^-5, when the FEC code is the (15,11) Hamming codes concatenated with rate-1 accumulator codes, while coded NS-32QAM performs 0.25 dB better than standard 32QAM.