An Exit-Chart Aided Design Procedure for Near-Capacity N-Component Parallel Concatenated Codes

Shannon´s channel capacity specifies the upper bound on the amount of bits per channel use. In this paper, we explicitly demonstrate that twin-component turbo codes suffer from a capacity loss, when the component code rate is less than unity, which is shown by exploiting the so-called area properties of Extrinsic Information Transfer (EXIT) charts. This capacity loss is unavoidable for twin-component turbo codes, when the overall turbo coding rate is less than 1/2, while multiple-component turbo codes are capable of overcoming it by using unity-rate component codes. In order to demonstrate that multiple-component turbo codes are capable of exhibiting a better asymptotic performance, the minimum Signal Noise Ratio (SNR) required for the EXIT charts to have open convergence tunnels is used as our metric, which is referred to as ´the open tunnel SNR threshold´. Furthermore, the employment of conventional two-dimensional EXIT charts is extended to facilitate the analysis of N-component turbo codes. Our results confirm that multiple-component turbo codes approach the Discrete-input Continuous-output Memoryless Channel´s (DCMC) capacity more closely and achieve a lower Bit Error Ratio (BER) than twin-component turbo codes at the same coding rate and the same complexity.