This letter proposes extended single parity check product codes and presents their empirical performances on a Gaussian channel by belief propagation (BP) decoding algorithm. The simulation results show that the codes can achieve close-to-capacity performance in high coding rate. The code of length 9603 and of rate 0.96 is only 0.77 dB away from the Shannon limit for a BER of 10-5.

Rate compatible (RC) codes are used for adaptive coding schemes or hybrid ARQ schemes in order to adapt varying channel conditions. This can improve overall service quality or the system throughput. Conventional RC codes have usually been designed on the basis of convolutional codes. This letter proposes an efficient RC code based on block codes. We use a high dimensional product code and divide it into the information block and a number of parity blocks. We form RC product codes using various combinations of these blocks. Because we can decode the RC product codes iteratively, these result in block turbo codes and they can be used efficiently for hybrid ARQ schemes.

This paper presents an iterative algorithm for decoding product codes based on syndrome decoding of component codes. This algorithm is devised to achieve an effective trade-off between error performance and decoding complexity. A simplified list decoding algorithm, which uses a modified syndrome decoding method, for linear block codes is devised to deliver soft outputs for iterative decoding of product codes. By adjusting the size of the list, the decoder can achieve a proper trade-off between decoding complexity and performance. Compared to the other iterative decoding algorithms for product codes, the proposed algorithm has lower complexity while offers at least the same performance, which is demonstrated by analyses and simulations. The proposed algorithm has been simulated for BPSK and 16-QAM modulations over both the additive white Gaussian noise (AWGN) and Raleigh fading channels. This paper also presents an efficient scheme for applying product codes and their punctured versions. This scheme can be implemented with variable packet size and channel data block.

In this paper, the iterative decoding of BCH product codes also called Block Turbo Codes (BTC) is evaluated for the HIPERLAN/2 OFDM system. Simulations show that expurgated BCH codes should be chosen as constituent codes in order to outperform the specified convolutional code. We also show that the bit-by-bit frequency interleaver has a big impact on the behaviour of the turbo decoding process and that increasing its size together with time diversity lead to good performance when compared to the convolutional code.

Two types of multicast error control protocols based on a product code structure with or without interleaving are considered. The performances of these protocols are analyzed on burst error channels modeled by Gilbert's two-state Markov chain. The numerical results reveal that the interleaving does not always succeed in improving the performance of the protocol proposed in Part .

A multicast error control protocol proposed by Metzner is generalized and the performance of the proposed protocol on random error channels (binary symmetric channels) is analyzed. The proposed protocol adopts an encoding procedure based on a product code structure, whith enables each destined user terminal to decode the received frames with the Reddy-Robinson algorithm. As a result, the performance degradation due to the re-broadcasting of the replicas of the previously transmitted frames can be circumvented. The numerical results for the analysis and the simulation indicate that the proposed protocol yields higher throughput and less degradation of throughput with an increase of the number of destined terminals.