On the distribution of residual errors of turbo codes and its application to concatenated codes

The residual errors of turbo decoding are studied in this paper. We define the error distribution function (EDF) or the error spectrum of turbo codes and give an approximate equation to obtain the EDF from the input redundancy weight enumerating function (IRWEF) under the AWGN channel. As a function of signal to noise ratio (SNR), the EDF is a useful tool in studying the property of residual errors. The study of EDF is also helpful when making the trade-off between the overall coding rate and the error correcting capability of an algebraic outer code, which is concatenated with a turbo code to lower the frame error rate.