Unfortunately this paper contains two errors with respect to Gallager's work on low density parity check codes. We gained the impression from the literature that \the sparse parity check codes studied by Gallager are bad," but this is in fact not the case. We also had the impression that Gallager's decoding algorithm was the same as Meier and Staaelbach's, and that our use of belief propagation...

We introduce upper bounds on the achievable rates of binary linear block codes under maximum-likelihood (ML) decoding, and lower bounds on the asymptotic density of their parity-check matrices; the transmission of these codes is assumed to take place over an arbitrary memoryless binary-input output-symmetric channel. The bounds hold for every sequence of binary linear block codes. The new bound...

We consider the design of convolutional codes and low-density parity-check (LDPC) codes with minimum-shift keying (MSK) when the receiver employs iterative decoding and demodulation. The main idea proposed is the design of coded schemes that are well matched to the iterative decoding algorithm being used rather than to hypothetical maximum-likelihood decoding. We first show that the design is c...

This paper presents high-performance encoder and decoder architectures for a class of Low Density Parity Check (LDPC) codes. The codes considered here are based on the Parallelly Concatenated Parity Check encoder structure. A major advantage of these codes is that the generator matrix and the parity check matrix are both sparse, which leads to efficient VLSI implementations for the encoder and ...