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The Extended Min-Sum (EMS) algorithm for non-binary low-density parity-check(LDPC) defined over an alphabet of size $q$ operates on truncated messages oflength $q'$ to achieve a complexity of the order $q'^2$. In contrast,Walsh-Hadamard (WH) transform based iterative decoders achieve a complexity ofthe order $q\log q$, which is much larger for $q'<<q$. In this paper, wedemonstrate that considerable savings can be achieved by letting WH baseddecoders operate on truncated messages as well. We concentrate on the direct WHtransform and compute the number of operations required if only $q'$ of the $q$inputs are non-zero. Our paper does not cover the inverse WH transform andhence further research is needed to construct WH based decoders that cancompete with the EMS algorithm on complexity terms.

Non-binary LDPC decoding using truncated messages in the Walsh-Hadamard domain