Power Allocation for the Base Matrix of Spatially Coupled Sparse Regression Codes

We investigate power allocation for the base matrix of a spatially coupled sparse regression code (SC-SPARC) for reliable communications over an additive white Gaussian noise channel. A conventional SC-SPARC allocates power uniformly to the non-zero entries of its base matrix. Yet, to achieve the channel capacity with uniform power allocation, the coupling width and the coupling length of the base matrix must satisfy regularity conditions and tend to infinity as the rate approaches the capacity. For a base matrix with a pair of finite and arbitrarily chosen coupling width and coupling length, we propose a novel power allocation policy, termed V-power allocation. V-power allocation puts more power to the outer columns of the base matrix to jumpstart the decoding process and less power to the inner columns, resembling the shape of the letter V. We show that V-power allocation outperforms uniform power allocation since it ensures successful decoding for a wider range of signal-to-noise ratios given a code rate in the limit of large blocklength. In the finite blocklength regime, we show by simulations that power allocations imitating the shape of the letter V improve the error performance of an SC-SPARC.