On the Weight Distribution of Some Turbo-Like Codes

Abstract

Parallel concatenated turbo codes are capable of near-capacity performance at moderate bit-error-rates, while serial concatenated turbo codes are capable of almost error-free performance at higher signal-to-noise ratios. It is desirable to have codes that achieve a combination of these characteristics. In attempting to lower the “error floor” of parallel concatenated turbo codes, we consider several hybrid concatenation schemes with parallel concatenated inner turbo codes serially concatenated with outer block and convolutional codes. The objective is for the outer code to “filter out” the bad input sequences for the inner turbo code and for the outer decoder to collaborate in iterative decoding with the inner turbo decoder. As one example, we consider using a rate 3/4 outer convolutional code and a rate 2/3 inner turbo code in an overall rate 1/2 hybrid concatenation scheme, and we obtain the exact weight distribution of this scheme for some typical interleaves and very short block lengths and compare these results to conventional rate 1/2 turbo codes. The hybrid scheme clearly has a superior weight distribution. We also consider another very interesting turbo-like coding scheme, a serial concatenation of three convolutional codes, and obtain the weight distribution of this scheme with an overall rate of 1/4, for some typical interleaves and very short block lengths. It is again clear that this code has a superior weight distribution compared to both a parallel concatenation of three convolutional codes and a serial concatenation of two convolutional codes with overall rate ¼. Because of their exceptional weight distributions, these schemes have the potential to outperform conventional turbo codes.