Decoder

Abstract—We consider the problem of transmitting correlated data after independent encoding to a central receiver through orthogonal channels. We assume that the channel state informa-tion is not known at the transmitter. The receiver has access to both the source correlation and the channel state information. We provide a generic framework for analyzing the performance of joint iterative decoding, using density evolution. Using dif-ferential evolution, we design punctured systematic LDPC codes to maximize the region of achievable channel conditions, with joint iterative decoding. The main contribution of this paper is to demonstrate that properly designed LDPC can perform well simultaneously over a wide range of channel parameters. Index Terms—LDPC codes, density evolution, correlated sources, non-systematic encoders, joint decoding, differential evolution. I. PROBLEM SETUP Consider the problem of transmitting the outputs of two discrete memoryless correlated sources, (U1, U2), to a cen-tral receiver through two independent discrete memoryless channels with capacities C1 and C2, respectively. The system model is shown in Figure 1. We will assume that the channels belong to the same channel family, and that each channel can be parametrized by a single parameter α (e.g., the erasure probability for erasure channels). The two encoders are not allowed to communicate. Hence they must use independent encoding functions, which map k input symbols (U1 and U2) to n1 and n2 output symbols (X1 and X2), respectively. The rates of the encoders are given by R1 = k/n1 and R2 = k/n2. The decoder receives (Y1,Y2) and makes an estimate of (U1,U2). This joint source-channel coding problem can be seen to be an instance of Slepian-Wolf coding [1] in the presence of a noisy channel