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 asymptoticminimum 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.