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.