Improved decoding of analog modulo block codes for noise mitigation

A drawback of digital transmission of analog signals is the unavoidable quantization error which leads to a limited quality even for good channel conditions. This saturation can be avoided by using analog transmission systems with discrete-time and quasi-continuous-amplitude encoding and decoding, e.g., Analog Modulo Block codes (AMB codes). The AMB code vectors are produced by multiplying a real-valued information vector with a real-valued generator matrix using a modulo arithmetic. Here, algorithms for improving the decoding performance are presented. The Lattice Maximum Likelihood (LML) decoder, a variant of the Discrete Maximum Likelihood (DML) decoder, is derived and analyzed. It refines the Zero Forcing (ZF) result if necessary, thus achieving near-ML signal quality with a reduced decoding complexity. A reduced complexity is essential for decoding high-dimensional code words. Additionally, pre- and post-processing methods are presented and analyzed, which increase the signal-to-distortion ratio (SDR) of the received symbols.