Joint channel estimation and decoding of LDPC codes with analog circuits
Hamed Farhadi, Farshad Lahouti · 2007
To decode LDPC coded frames by the Belief Propagation (BP) algorithm successfully, it is necessary to prepare appropriate soft inputs for the decoder according to the channel SNR, which is unknown to the receiver in general. Also, to have a full analog receiver, of interest in practical applications, it is necessary to design analog circuits that receive the demodulator soft outputs and prepare appropriate soft inputs for the analog decoder. In this work, we study the sensitivity of the performance (BER & FER) of the LDPC codes using the BP decoding in the presence of channel SNR mismatch. Then, we introduce soft metrics, including the minimum absolute value of LLR at the decoder outputs, which can be extracted from the decoder soft outputs easily, and have the same dynamic as the BER under the estimated channel SNR mismatch. Also, we show that the minimum value of the BER occurs when the minimum absolute value of the decoder output LLR reaches its maximum value. Next, we propose a graph based algorithm which is composed of a BP LDPC decoder and a stochastic gradient-type recursive channel estimator. The estimator nodes attempt to increase the minimum absolute LLR value of the decoder soft outputs adaptively by changing the estimated channel reliability. The circuits of the check nodes and the variable nodes of the LDPC decoder are based on the conventional voltage mode Gilbert multiplier for LLR domain decoding. Therefore, we focus on the design of the analog circuit for the implementation of the building blocks of the estimator nodes. The designed circuits include an interface between the decoder and the estimator nodes, a metric extractor, and a decision circuit to determine the direction of the estimated channel reliability variations, and a recursive update circuit as the core of the estimator.