Analysis and Design of Tuned Turbo Codes

It has been widely observed that there exists a fundamental tradeoff between the minimum (Hamming) distance properties and the iterative decoding convergence behavior of turbo-like codes. While capacity-achieving code ensembles typically are asymptotically bad in the sense that their minimum distance does not grow linearly with block length, and they therefore exhibit an error floor at moderate-to-high signal-to-noise ratios, asymptotically good codes usually converge further away from channel capacity. In this paper, we introduce the concept of tuned turbo codes, a family of asymptotically good hybrid concatenated code ensembles, where asymptotic minimum distance growth rates, convergence thresholds, and code rates can be tradedoff using two tuning parameters:
$\lambda $
and
$\mu $
. By decreasing
$\lambda $
, the asymptotic minimum distance growth rate is reduced in exchange for improved iterative decoding convergence behavior, while increasing
$\lambda $
raises the asymptotic minimum distance growth rate at the expense of worse convergence behavior, and thus, the code performance can be tuned to fit the desired application. By decreasing
$\mu $
, a similar tuning behavior can be achieved for higher rate code ensembles.