In this work, we propose a coding strategy designed to enhance the throughput of hybrid ARQ (HARQ) transmissions over i.i.d. block-fading channels with the channel state information (CSI) unknown at the transmitter. We use a joint packet coding where the same channel block is logically shared among many packets. To reduce the complexity, we use a two-layer coding where, first, packets are first coded by the binary compressing encoders, and the results are then passed to the conventional channel encoder. We show how to optimize the compression rates on the basis of the empirical error-rate curves. We also discuss how the parameters of the practical turbo-codes may be modified to take advantage of the proposed HARQ scheme. Finally, simple and pragmatic rate adaptation strategies are developed. In numerical examples, our scheme is compared to the conventional incremental redundancy HARQ (IR-HARQ), and it yields a notable gain of 1-2 dB in the region of high throughput, where HARQ fails to provide any improvement.