DIMACS Series in Discrete Mathematics and Theoretical Computer Science Hybrid ARQ with Random Transmission Assignments

In mobile packet data and voice networks, a special coding scheme, known as the incremental redundancy hybrid ARQ (IR HARQ), achieves higher throughput efficiency than ordinary turbo codes by adapting its error correcting code redundancy to fluctuating channel conditions characteristic for this application. An IR HARQ protocol operates as follows. Initially, the information bits are encoded by a “mother” code and a selected number of parity bits are transmitted. If a retransmission is requested, only additional selected parity bits are transmitted. At the receiving end, the additional parity bits are combined with the previously received bits, allowing for an increase in the error correction capacity. This procedure is repeated after each subsequent retransmission request until the entire codeword of the mother code is transmitted. A number of important issues such as error rate performance after each transmission on time varying channels, and rate and power control are difficult to analyze in a network employing a particular HARQ scheme, i.e., a given mother code and given selection of bits for each transmission. By relaxing only the latter constraint, namely, by allowing random selection of the bits for each transmission, we provide very good estimates of error rates allowing us to address to a certain extent the rate and power control problem.