Partial Spatial Coupling of LDPC Codes: Reducing the Gap to Capacity by Improving the Rate

Abstract

A different approach for constructing protograph-based spatially coupled low-density parity-check (SC-LDPC) codes is proposed. Instead of lifting multiple copies of an identical SC-LDPC protograph at the lifting stage of code construction, we divide the copies into fractions α ∈ [0,1] SC-LDPC protographs and β = 1-α uncoupled sequence of block LDPC protographs. The permutations in the edge bundles formed by two different protograph structures follow the multi-edge-type framework. The rate loss associated with SC-LDPC codes is reduced, and we obtain code ensembles with flexible rates, by varying β. We call these codes partial spatially coupled (PSC) LDPC codes, and through density evolution, we show that for data transmission over the binary erasure channel, the gap between channel capacity and thresholds of these codes is smaller as compared to SC-LDPC codes. The main bottleneck in the practical implementation of SC-LDPC codes is the rate loss. Conventionally, the rate loss can be reduced by taking large coupling length L , which however increases the decoding complexity. The proposed PSC-LDPC codes mitigate this tradeoff. Furthermore, these codes can also be decoded by the windowed decoder (WD), and through Monte Carlo simulations, we show that the WD performance of PSC-LDPC codes is better than that of SC-LDPC codes.