Soft-input reconstruction of binary transmitted quantized overcomplete expansions

In this letter, we propose a soft-decoding method for quantized overcomplete frame expansions that are binary transmitted through noisy channels. The frame expansions can be viewed as real-valued block codes that are directly applied to waveform signals prior to quantization. The explicit redundancy introduced in the continuous amplitude domain is exploited by the decoder in two stages. First, the index-based redundancy is used by a soft-input soft-output source decoding approach that outputs decoded symbols together with their reliability information. In a second stage, the soft information on the symbols and the structure of the introduced redundancy are used to correct errors. The performance of the proposed approach is evaluated for different code constructions based on the discrete Fourier transform (DFT), the discrete cosine transform (DCT), and the discrete Hadamard transform (DHT), and is compared to standard approaches without soft decoding.