Codes for Second and Third Order GH - ARQSchemesLuca

| In the usual ARQ (Automatic-Repeat-Request) communication protocols, when the receiver detects the presence of errors in a received message, it requests the retrans-mission of another copy of the message, and the process continues until an uncorrupted copy reaches the destination. If the quality of the channel is poor, the number of retransmissions may become very large. In order to improve the eeciency at large channel error rates, some new techniques known as Type-II Hybrid ARQ Schemes have recently been proposed. In these techniques the transmitter does not retransmit the message encoded as in the rst transmission: it sends instead additional redundancy that is decoded at the destination along with the previously received information to allow error correction. In this paper a new kind of Type-II Hybrid ARQ transmission scheme is proposed. The copies of the message are encoded in diierent ways, so that each copy has the same information content, and the knowledge of any subset of the copies allows error correction. This transmission scheme is well suited to broadcast as well as for point to point communications. We have obtained trough computer search a family of optimum and quasi-optimum codes for the proposed transmission scheme. They are described along with new decoding techniques of remarkable simplicity and eeectiveness. These codes allow a message to be encoded in up to three diierent ways, and they are shown to be simple to encode and decode and to perform well over channels aaected by error bursts.