Error-correcting code on a cactus:A solvable model

An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica-symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes.

An adaptive code position modulation scheme for wireless sensor networks

In this letter, an energy-efficient adaptive code position modulation scheme is proposed for wireless sensor networks to provide the relatively stable bit error ratio (BER) performance expected by the upper layers. The system is designed with focus on the adaptive control of transmission power, which is adjusted based on the measured power density of background noise. Interfaces among the modulation module, packet scheduling module and upper layer are provided for flexible adjustments to adapt to the background noise and deliver expected application quality. Simulations with Signal Processing Worksystem (SPW) validate the effectiveness of the scheme. © 2005 IEEE.