Converging ARQ schemes

The parity check matrix of an (n, k, t) Hnear error-correcting code provides a unique mapping between binary vectors of length n, whose Hamming weight does not exceed t, and binary vectors of length (n ’ k), which are the syndrome obtained by multiplying the vector of length n by the parity check matrix. This enables the ‘compression’ of binary vectors having a limited Hamming weight. It is shown in the paper how this principle can be applied in ARQ schemes, where, upon detection of an error in a received message, further retransmitted messages can be made shorter from one retransmission to the next.