Two incremental redundancy hybrid ARQ (IR-code. Initially, only the systematic part of the codeword and HARQ) schemes are compared: one is based on LDPC code a selected number of parity bits are transmitted. The selected ensembles with random transmission assignments, the other parity bits together with the systematic bits form a codeword of is based on recently introduced Raptor codes. A number of a bits totherwtte sematic bis codeword important issues, such as rate and power control, and error rate a puctredemotherd. Deodngfissodis perfomed, performance after each transmission on time varying binary-at the receiving end. If a retransmission is requested, the input, symmetric-output channels are addressed by analyzing transmitter sends additional parity bits possibly under different performance of LDPC and Raptor codes on parallel channels. channel conditions or at different power. Decoding is again The theoretical results obtained for random code ensembles are attempted at the receiving end, where the new parity bits are tested on several practical code examples by simulation. Both theoretical and simulation results show that both LDPC and combined with those previously received. The procedure is Raptor codes are suitable for HARQ schemes. Which codes would repeated after each subsequent retransmission request until all make a better choice depends mainly on the width of the signal-the parity bits of the mother code are transmitted. to-noise operating range of the HARQ scheme, prior knowledge A historic overview of hybrid ARQ schemes up to 1998, can of that range, and other design parameters and constraints be found in [1]. Recent interest in the schemes comes from dictated by standards. the quest for reliable and efficient transmission under fluctuat-
An LDPC code based hybrid ARQ scheme with random transmission assignments is analyzed. The spectrum properties of LDPC code ensembles that are necessary for this analysis are derived. Very good estimates of maximum-likelihood decoding error rates after each transmission are provided. The results are tested on practical code examples by simulation.
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