Pruned Hypothesis Parallel Message Passing for List-Based ML Approximation in Unit-Rate Reception

This paper presents a receiver-centric detection architecture formulated as a list-based approximation to maximum-likelihood (ML) detection under unit-rate transmission of information bits. For each k-bit payload, the receiver enumerates 2k information hypotheses and embeds each hypothesis into a higher-dimensional (k, n) linear block code. With receiver access to the code description (e.g., a look-up table or an equivalent representation), an orthogonality/consistency screening metric enables substantial pruning prior to refinement, so refinement is performed only for retained hypotheses. For each retained hypothesis, a one-shot message-passing update on the associated Tanner graph is used as a refinement operator. Final detection is performed by ML selection over the refined candidate set using the physical-channel likelihood. Performance is benchmarked against: (i) uncoded ML under memoryless AWGN, and (ii) an ML-of-architecture oracle defined as full-search selection over the refined candidates. Pruning behavior is quantified via the average list size L versus Eb/No. Simulation results are reported for receiver-only embeddings such as (8,24) and (8, 96) low-density parity-check (LDPC) codes. In addition to the memoryless additive white Gaussian noise (AWGN) reference, the paper introduces a pilot-aided two-tap multipath extension (real BPSK) in which a short known preamble supports channel estimation and the final ML-of-architecture selection uses the corresponding intersymbol interference (ISI) likelihood. This extension illustrates how the same receiver pipeline applies to non-ideal channels by substituting the physical-channel likelihood, and motivates the approach as an implementable alternative when exact joint ML becomes impractical due to exponential hypothesis growth and/or additional unknown parameters, at the expense of requiring full receiver knowledge of the codebook.