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The problem of efficient maximum-likelihood soft decision decoding of binary BCH codes is considered. It is known that those primitive BCH codes whose designed distance is one less than a power of two, contain subcodes of high dimension which consist of a direct sum of several identical codes. We show that the same kind of direct-sum structure exists in all(More)
A novel deep learning method for improving the belief propagation algorithm is proposed. The method generalizes the standard belief propagation algorithm by assigning weights to the edges of the Tanner graph. These edges are then trained using deep learning techniques. A well-known property of the belief propagation algorithm is the independence of the(More)
We propose a new type of short to moderate block-length, linear error-correcting codes, called moderate-density parity-check (MDPC) codes. The number of one’s of the parity-check matrix of the codes presented is typically higher than the number of one’s of the parity-check matrix of low-density paritycheck (LDPC) codes. But, still lower than those of the(More)
Abstmct-Multilevel constructions of the binary Golay code and the Leech lattice are described. Both constructions are based upon the prvjection of the Golay code and the Leech lattice onto the (6,3,4) hexacode over GF(4). However, unlike the previously reported constructiods, the new multilevel constructions make the three levels independent by way of using(More)
In this paper, the trellis representation of nonlinear codes is studied from a new perspective. We introduce the new concept of entropy/length profile (ELP). This profile can be considered as an extension of the dimension/length profile (DLP) to nonlinear codes. This elaboration of the DLP, the entropy/length profiles, appears to be suitable to the analysis(More)