A Genie-Aided Approach to Error Floor Estimation for Spatially Coupled Serially Concatenated Codes

As subclasses of spatially coupled turbo-like codes (SC-TCs), hybrid coupled serially concatenated codes (HC-SCCs) and spatially coupled serially concatenated codes (SC-SCCs) are attractive for streaming applications. However, it is a long-standing problem to estimate the error floors of HC-SCCs and SC-SCCs. To tackle this problem, we present a genie-aided approach in this paper. Specifically, we first show that the performance of a given HC-SCC or SC-SCC can be lower bounded by a hybrid concatenated code which is obtained by assuming the coupled sub-sequences are known or partially known. Second, we derive the average input-output weight enumerating functions (IOWEF) of the hybrid concatenated code ensembles corresponding to SC-SCC and HC-SCC. Third, the obtained IOWEFs are used to estimate the error floors. The numerical results show the tightness of the proposed method in estimating the error floors of SC-SCCs and HC-SCCs. We then use the proposed method to analyze the impact of the memories of the component convolutional codes on error floor. Particularly, we show that, for a given total memory order
$v$
, the lowest error floor is achieved by selecting the memories of the outer and inner component convolutional codes as
$\lceil \frac {v}{2} \rceil $
and
$\lfloor \frac {v}{2} \rfloor $
, respectively. In addition, for both SC-SCCs and HC-SCCs, reduced error floor can be achieved by increasing the outer coupling memory.