Surpassing Purely Digital Transmission: A Simplified Design of Hybrid Digital Analog Codes

Abstract:
One problem of conventional digital transmission systems that transmit real-valued source symbols is that the transmission fidelity always saturates for channels that have attained the design channel quality (worst-case channel condition); this saturation is caused by the irreversible error introduced by the source coder. Even though hybrid digital analog (HDA) codes address this problem by additionally transmitting the inherent quantization error by using analog methods, the design and the decoding of these HDA codes is complex or even impossible for long block lengths. Thus, the aim of this study is to introduce a new way to design HDA codes using well-known digital codes. Another objective is to theoretically and empirically compare the proposed design with the conventional purely digital transmission systems. This study applied Monte Carlo simulations with Reed- Solomon codes or convolutional codes as the digital part and LMMSE estimation in the analog part of the HDA system. The simulation results agreed well with the theoretical considerations. Since the proposed design uses well-established, excellent digital codes that support long block lengths, the design and decoding of HDA codes is simplified. The inherent error introduced by the source coder is reduced by combining these digital codes with analog transmission, thereby eliminating the saturation of the transmission fidelity. The newly proposed HDA system surpasses the purely digital transmission system at all channel qualities. Index Terms — Hybrid Digital Analog (HDA), Reed-Solomon code, convolutional code, LMMSE estimator, joint MMSE decoding.