Analysis of the dynamics of iterative interference cancellation in iterative decoding
Problems of Information Transmission
Soft-decision majority decoding of Reed-Muller codes
IEEE Transactions on Information Theory
Soft-decision decoding of Reed-Muller codes: a simplified algorithm
IEEE Transactions on Information Theory
Soft-decision decoding of Reed-Muller codes: recursive lists
IEEE Transactions on Information Theory
Error Exponents for Recursive Decoding of Reed–Muller Codes on a Binary-Symmetric Channel
IEEE Transactions on Information Theory
| Hi-index | 754.84 |
Error exponents are studied for recursive and majority decoding of general Reed-Muller (RM) codes RM (r, m) used on the additive white Gaussian noise (AWGN) channels. Both algorithms have low complexity and correct many error patterns whose weight exceeds half the code distance. Decoding consists of multiple consecutive steps, which repeatedly recalculate the input symbols and determine different information symbols using soft-decision majority voting. For any code RM (r, m), we estimate the probabilities of the information symbols obtained in these recalculations and derive the analytical upper bounds for the block error rates of the recursive and majority decoding. In the case of a low noise, we also obtain the lower bounds and show that the upper bounds are tight. For a higher noise, these bounds closely approach our simulation results.