Construction and Performance of q-ary Turbo Codes for use with M-ary Modulation Techniques

This paper describes a construction technique for q-ary Turbo Codes that computes good recursive systematic convolutional q-ary constituent codes with constraint length ν ≤ 5 for q = 2, m = 2 and 3. The construction technique, based on the algorithm in [5], determines the codes with maximum di for i = 2, 3, and 4 and minimum codeword multiplicity, where di is the minimum weight of all code sequences with input weight i. Due to the large number of encoder states involved, standard weight distribution calculations are difficult. The construction algorithm employed is a computer search that generates all possible terminating input sequences of weight 2, 3, and 4 to use as inputs to the set of allowable encoders. The best codes with maximum di and minimum multiplicity are determined. The performance of these Turbo codes using M-ary (M = 4, 8) non-coherent modulation (FSK) and Differentially Coherent PSK (DPSK) is computed by simulation and performance bounds assuming the parallel concatenation of two constituent codes. M-ary FSK or DPSK with q-ary Turbo Coding can provide an efficient modulation / coding solution. The emphasis is on matching the modulation alphabet with the Turbo coding alphabet (q = M) to implement simple modulation / coding approaches that perform at a lower required Eb/No and greater bandwidth efficiency than current coding approaches using these modulation techniques.