Generalized Low-density Research Articles

Distributed Generalized Low-Density Codes for Wireless Relay Networks

Distributed generalized low-density (GLD) codes are proposed for cooperative networks with multiple relays. Specifically, every relay can decode and forward one or several constituent codes of the GLD code to cooperatively construct a distributed GLD code using the partial error-detecting and error-correcting capabilities of the GLD code. The scheme can be flexibly adjusted to the variation of the relay number and work effectively under both perfect and imperfect source-relay channels verified by simulations.

Distributed Generalized Low-Density Codes for Multiple Relay Cooperative Communications

As a class of pseudorandom error correcting codes, generalized low-density (GLD) codes exhibit excellent performance over both additive white Gaussian noise (AWGN) and Rayleigh fading channels. In this paper, distributed GLD codes are proposed for multiple relay cooperative communications. Specifically, using the partial error detecting and error correcting capabilities of the GLD code, each relay node decodes and forwards some of the constituent codes of the GLD code to cooperatively form a distributed GLD code, which can work effectively and keep a fixed overall code rate when the number of relay nodes varies. Also, at relay nodes, a progressive processing procedure is proposed to reduce the complexity and adapt to the source-relay channel variations. At the destination, the soft information from different paths is combined for the GLD decoder thus diversity gain and coding gain are achieved simultaneously. Simulation results verify that distributed GLD codes with various number of relay nodes can obtain significant performance gains in quasistatic fading channels compared with the strategy without relays and the performance is further improved when more relays are employed.

An Ensemble of Iteratively Decodable Codes Constructed Based on a Superposition Method

In this paper, the construction of new families of error-correcting codes adapted from Boutros and Lentmaier's generalized low-density (GLD) codes, which we called generalized irregular low-density (GILD) codes, is investigated. By introducing irregular base matrices, significant improvements on Boutros and Lentmaier's results are achieved. Two cases are considered; in the first case, the same constituent code is used, and in the second case, different constituent codes are used. It is proved by an ensemble performance argument that these codes exist and are asymptotically good in the sense of the minimum-distance criterion. It is also proved that the performance of GILD codes approaches the binary symmetric channel capacity limit. Iterative decoding of GILD codes for communication over an additive white Gaussian noise channel is also studied. The high flexibility in selecting the parameters of GILD codes and their better performance and higher rate make them more attractive than GLD codes, and hence, suitable for small and medium block lengths forward-error-correcting schemes. Comparisons of simulation results between some GILD codes and some good low-density parity-check codes show very close performances

Application of efficient Chase algorithm in decoding of generalized low-density parity-check codes

We consider the iterative decoding of generalized low-density (GLD) parity-check where, rather than employ an optimal subcode decoder, a Chase (1972) algorithm decoder more commonly associated with turbo product codes is used. GLD are low-density graph in which the constraint nodes are other than single parity-checks. For extended Hamming-based GLD codes, we use bit error rates derived by simulation to demonstrate this new strategy to be successful at higher code rates. For long block lengths, good performance close to capacity is possible with decoding costs reduced further since the Chase decoder employed is an efficient implementation.

On generalized low-density parity-check codes based on Hamming component codes

In this paper we investigate a generalization of Gallager's (1963) low-density (LD) parity-check codes, where as component codes single error correcting Hamming codes are used instead of single error detecting parity-check codes. It is proved that there exist such generalized low-density (GLD) codes for which the minimum distance is growing linearly with the block length, and a lower bound of the minimum distance is given. We also study iterative decoding of GLD codes for the communication over an additive white Gaussian noise channel. The performance in terms of the bit error rate, obtained by computer simulations, is presented for GLD codes of different lengths.