There has been a growing interest in designing neural-network based decoders (or neural decoders in short) for communication systems. In the prior work, we cast the problem of decoding an (n, k) block code as a single-label classification problem, and it is shown that the performance of such single-label neural decoders closely approaches that of the corresponding maximum likelihood soft-decision (ML-SD) decoders. The main issue is that the number of output nodes of single-label neural decoders increases exponentially with k, making it prohibitive to decode a code with medium or large dimension. To address this issue, we first explore a multi-label classification based neural decoder for block codes, in which the number of output nodes increases linearly with k. The complexity of the multi-label neural decoder is lower, but the performance is still close to that of the ML-SD decoder. We also consider concatenating a high-rate short-length outer code with the original code as the inner code. The proposed concatenated decoding architecture consists of a multi-label neural decoder for the inner code and a single label neural decoder for the outer code. The results demonstrate that the concatenated decoding approach leads to better bit and block error performance as compared to a benchmark soft-decision decoder. We note that the overall size of the concatenated neural decoder is close to that of the single-label neural decoder.
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