Incremental Redundancy via Check Splitting

A new method of creating rateless codes for noisy channels is presented. Unlike puncturing, where every punctured variable disables several checks, or extending, which creates many cycles in the code graph or creates parity checks with insufficient weight, the proposed method uses check splitting to lower the rate of the code. Check splitting operates by replacing a row r of maximum weight in the parity check matrix with two new rows s₁ and s₂, of approximately equal weight and with s₁opluss₂=r. This causes the check-node degree-distribution to remain fairly concentrated and prevents cycles from forming as the rate decreases. This scheme performs closer to capacity than Raptor codes, it can use a linear-time-encodable code such as a repeat-accumulate code, and it has nearly constant decoding complexity per information bit per iteration, independent of the effective code rate