Analysis and Design of Tuned Turbo Codes

TL;DR

This paper introduces tuned turbo codes, a family of hybrid codes that balance minimum distance growth and decoding convergence through tunable parameters, enabling tailored performance for different applications.

Contribution

It proposes a novel class of asymptotically good turbo-like codes with adjustable trade-offs between distance properties and decoding behavior using two parameters.

Findings

Tuned turbo codes allow flexible performance tuning.

Decreasing λ improves convergence at the cost of minimum distance.

Increasing λ enhances minimum distance but worsens convergence.

Abstract

It has been widely observed that there exists a fundamental trade-off 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 traded-off 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.