Converging ARQ schemes

The parity check matrix of an (n, k, t) linear 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.