Performance of turbo-decoded product codes used in multilevel coding

A powerful coding scheme based on multilevel coding and using a product code on the first partitioning level is proposed. The multistage decoder takes advantage of the iterative decoding of the product code to achieve a high coding gain. This coding scheme is compared to the one using the product code in a pragmatic approach with a Gray mapping. Results show that in the range of high bit error rates (BER greater than 10^-7, a product code having a high code rate (R>0.8) associated with a Gray mapping is the best solution. For high transmission rate applications, in which the required BER is lower than 10^-7, multilevel coding with a turbo-decoded product code is the recommended solution