Fractional Doping of Protograph-Based Spatially Coupled LDPC Codes

In this paper, we investigate ways to mitigate the problem of decoder error propagation (DEP) in sliding window decoding (SWD) of protograph-based spatially coupled low- density parity-check (SC-LDPC) codes for large frame length or streaming applications. In particular, in order to avoid subdividing a long frame into a series of shorter frames by using termination to combat DEP, we consider altering the code design by introducing occasional doped symbols into the encoded sequence, where the doping is accomplished by fixing the values of all or some of the variable nodes (VNs) at certain positions in the protograph.An important practical consideration in many applications is the ability to use systematic encoding. This necessitates that no more than a fraction of the VNs at any given position can be doped, i.e., that fractional doping be employed. We begin by showing numerically that full doping of a single position in the protograph of a long frame improves performance relative to that of terminating the frame at half its length. We then show that fractional doping of consecutive VN positions at a given location in the protograph is comparable to full doping. We also show that spreading fractionally doped positions over multiple locations in the protograph results in additional gains, where the effective code rate of a doped frame is always at least as high as that of the shorter terminated frame.