Buffering requirements for variable-iterations LDPC decoders

Low-density parity-check (LDPC) decoders, like iterative decoders for other block codes, can be designed to stop after a variable number of iterations, dependent on the difficulty of decoding particular noisy received words, also called frames. The number of iterations the decoder spends on a given frame determines both the probability of successful decoding, and the time expended. But whereas the speed of an LDPC decoder without a buffer is determined by its most difficult frames, the speed of a variable-iterations decoder with sufficient buffering approaches that determined by frames of average difficulty. It is relatively straightforward to analyze this as a D/G/1 queuing problem combined with empirically measured probability distributions of iteration counts for specific LDPC codes. Our analysis parallels that of other researchers, e.g., (J. Vogt and A. Finger, 2001), (G. Bosco et al., 2005), (M. Rovini and A. Martinez, 2007), and examines the resulting implications on LDPC decoder design choices. We find that a buffer large enough to hold only B = 2 or 3 additional frames is sufficient to achieve near optimal performance. We prove a strong monotonicity condition: not only does a variable-iterations decoder with buffer size B +1 frames outperform one with buffer size B in terms of average error rate, every single frame is guaranteed to receive at least as many iterations from the decoder with the larger buffer, if needed. Significantly, at low error rates, a variable-iterations decoder with buffer size B can keep pace with an input data rate B +1 times faster than a fixed-iterations decoder with the same processing speed.