Coded QAM using a binary convolutional code

The motivation is to utilize commercially available high-speed, low-cost, single-VLSI-chip binary-encoding/Viterbi-decoding systems (codecs). A Gray code is used to map the encoder output to the QAM constellation, transforming the large Hamming distance (HD) of the binary code into a large squared Euclidian distance of (SED) of CQAM and providing the basis for a simple, effective way to generate the binary metrics used for binary Viterbi decoding. Although the scheme may be generalized to any 2^2k-QAM, the discussion focuses on the design of 16-ary CQAM with a rate-3/4 punctured convolutional code of constraint length 7. A binary metric generation method is used so that no modification of the existing VLSI codec chips is required. This method, in conjunction with eight-level quantization for the binary metric, is shown to be suboptimum with little loss in signal-to-noise ratio compared to direct use of M-ary unquantized metric. Since the overall system is nonlinear, both worst-case and average performance are considered. Analytical and Monte Carlo simulation results are presented