Spatially-Coupled Serially Concatenated Codes with Periodic Convolutional Permutors

Spatially-coupled serially concatenated codes (SC-SCCS) are a class of turbo-like codes constructed by interconnecting a sequence of SCCS using a set of block permutors. At short block lengths, however, the bit-error-rate (BER) performance of SC-SCCS constructed by independent block permutors exhibits a high error floor. In this paper, we propose an alternative method for constructing SC-SCCS to mitigate this problem. Particularly, we use a family of periodically time-varying blockwise convolutional permutors with flexible block length. We derive these convolutional permutors from a block permutor of an optimized spread by applying an unwrapping procedure. We prove that for any chosen block length, the unwrapping procedure preserves the spread of the original block permutor. We further present an efficient implementation method for the blockwise convolutional permutor that derives the permutation indices directly from those of the underlying block permutor. Considering both S-random permutors and quadratic permutation polynomial (QPP) permutors, we perform BER simulations for SC-SCCS with decoding latencies 4096 and 16384. Numerical results show that SC-SCCS based on the proposed convolutional permutors have no visible error floor, which is especially notable at short block lengths.