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The authors study network-coded receiver cooperation for a wireless system comprising a remote sender and a set of local receivers. Network codes based on GF(2q) randommixing are complex and prone to errors. Sparse binary random-mixing is considerably simpler, but for it to be space preserving requires the involvement of a huge number of source packets (vectors). They propose a novel strategy of offset sparse binary random-mixing (OSBram), in which the source vectors are firstly circularly shifted, each by a different random offset, before being XORed. This simple strategy cleverly compensates the low degree of the binary field by the large dimension of the vector space, ensure (near) linear independence of random binary super-positions, and finds solid structural support from the well-known class of quasi-cyclic low-density parity-check codes.
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