We introduce multiple turbo codes and a suitable decoder structure derived from an approximation to the maximum a posteriori probability (MAP) decision rule, which is substantially different from the decoder for two-code-based encoders. We developed new rate 1/3 and 2/3 constituent codes to be used in the turbo encoder structure. These codes, for 2 to 32 states, are designed by using primitive polynomials. The resulting turbo codes have rates b/n, b=1, 2 and n=3, 4, and include random interleavers for better asymptotic performance. A rate 2/4 code with 16QAM modulation was used to realize a turbo trellis coded modulation (TTCM) scheme at 2 bit/sec/Hz throughput, whose performance is within 1 dB from the Shannon limit at a BER=10/sup -5/.