A distance spectrum interpretation of turbo codes

TLDR

The study investigates turbo code performance by analyzing its distance spectrum. The authors increase the code’s free distance by employing primitive feedback polynomials. The analysis shows that turbo codes’ error floor arises from low free distance, can be reduced by enlarging the interleaver, and that spectral thinning of low‑weight codewords makes the free‑distance asymptote the dominant performance factor at low to moderate SNR.

Abstract

The performance of turbo codes is addressed by examining the code's distance spectrum. The "error floor" that occurs at moderate signal-to-noise ratios is shown to be a consequence of the relatively low free distance of the code. It is also shown that the "error floor" can be lowered by increasing the size of the interleaver without changing the free distance of the code. Alternatively, the free distance of the code may be increased by using primitive feedback polynomials. The excellent performance of turbo codes at low signal-to-noise ratios is explained in terms of the distance spectrum. The interleaver in the turbo encoder is shown to reduce the number of low-weight codewords through a process called "spectral thinning." This thinned distance spectrum results in the free distance asymptote being the dominant performance parameter for low and moderate signal-to-noise ratios.