Design of LDPC codes with tunable slope of their EXIT charts
G. Montorsi · 2016
In this paper we consider the problem of designing LDPC codes to be used in bit turbo-receivers, where an outer binary (turbo) decoder iterates with a bit-detector computing LLR of coded bits from the channel outputs. This receiver structure has been proposed for several scenarios, including systems for high order modulations, MIMO, ISI, and Multi User systems. It has been shown that the bit turbo-receiver provides performance close to the optimal receiver if the bit-detector EXIT chart “matches” that of the outer code. Motivated by the observation that most bit-detector EXIT charts exhibit an almost linear behavior we then introduce the “slope” of the EXIT chart as a new parameter for the LDPC design. A family of binary LDPC codes having the possibility of tuning not only the rate, but also the slope of their EXIT chart, as well as the decoder complexity, is then an ideal candidate for being considered in future advanced transmission systems where the bit turbo-receiver will replace the more common BICM receiver that does not consider possible iterations with the bit detector. In this paper we provide an efficient algorithm for the design of LDPC codes ensembles with excellent performances with those constraints and derive some conclusions. It is shown that with a given performance threshold the complexity of LDPC decoder actually decreases when increasing the target slope, confirming the already observed fact that bit turbo-receiver requires weaker outer codes.