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Reed-Muller (RM) codes are one of the oldest families of codes. Recently, a recursive projection aggregation (RPA) decoder has been proposed, which achieves a performance that is close to the maximum likelihood decoder for short-length RM codes. One of its main drawbacks, however, is the large amount of computations needed. In this paper, we devise a new algorithm to lower the computational budget while keeping a performance close to that of the RPA decoder. The proposed approach consists of multiple sparse RPAs that are generated by performing only a selection of projections in each sparsified decoder. In the end, a cyclic redundancy check (CRC) is used to decide between output codewords. Simulation results show that our proposed approach reduces the RPA decoders computations up to $80%$ with negligible performance loss.
The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain families of
The famous Barnes-Wall lattices can be obtained by applying Construction D to a chain of Reed-Muller codes. By applying Construction ${{D}}^{{(cyc)}}$ to a chain of extended cyclic codes sandwiched between Reed-Muller codes, Hu and Nebe (J. London Ma
New quaternary Plotkin constructions are given and are used to obtain new families of quaternary codes. The parameters of the obtained codes, such as the length, the dimension and the minimum distance are studied. Using these constructions new famili
We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes our method exploits code symme
This paper presents a novel successive factor-graph permutation (SFP) scheme that significantly improves the error-correction performance of Reed-Muller (RM) codes under successive-cancellation list (SCL) decoding. In particular, we perform maximum-l