Parallel Message Passing Decoders for Uncoded Transmitted Data: Towards the Unit Code Rate

This paper aims to maximize the information transmission rate by eliminating channel redundancy while still enabling reliable recovery of uncoded data. It is shown that parallel message-passing decoders can recover uncoded transmitted bits by increasing only the receiver-side computational complexity. In the proposed architecture, the $k$ transmitted information bits are embedded into a higher-dimensional linear block code at the receiver, and appropriately valued log-likelihood ratios (LLRs) are assigned to the parity positions. One-shot parallel decoding is performed across all hypotheses in the codebook, and the final decision is obtained by minimizing an orthogonality-based energy criterion between the decoded vector and the complement of the code space. For a fixed $(8,24)$ linear block code, the decoding behavior is investigated as a function of the parity-bit LLR magnitude. Increasing the parity LLR magnitude introduces an artificial reliability that improves hypothesis separation in the code space and yields a sharper waterfall region in the bit-error-rate (BER) curves. This increase in parity LLR also induces a systematic rightward shift of the BER curves, which does not correspond to a physical noise reduction and must therefore be compensated for fair performance comparison. After proper compensation, it is observed that increasing the parity LLR improves decoding performance up to a point where it can surpass the performance of conventional LDPC decoding with iterative processing. In principle, arbitrarily strong decoding performance can be approached by increasing the parity LLR magnitude; however, the maximum usable value is limited by numerical instabilities in practical message-passing implementations. Overall, the results demonstrate that strong decoding performance can be achieved without transmitting redundancy or employing high-dimensional coding at the transmitter, relying instead on receiver-side processing and controlled parity reliability over an additive white Gaussian noise (AWGN) channel.