Improving the BER performance of turbo codes with short frame size based on union bound

In order to improve the bit error rate(BER) performance of turbo codes with short frame size at a wide range of signal to noise ratio(SNR),a new method by optimizing the bit energy is proposed.At first,a formula derived from the Union Bound is introduced.It describes the relations between the bit error rate distribution and the minimum weight distribution.And then,by mathematically optimizing the formula,the energy for every bit of the codeword is optimized to achieve the minimum BER at high SNR region.At last,an adjustable parameter is employed to compensate the degradations of BER at low and moderate SNR regions.Case studies indicate that the improvements of BER for turbo codes with short frame size are significant at a wide range of SNR.