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 a SC-SPARC.

翻译：我们研究用于加性高斯白噪声信道上可靠通信的空间耦合稀疏回归码（SC-SPARC）基矩阵的功率分配问题。常规SC-SPARC对其基矩阵的非零条目进行均匀功率分配。然而，为通过均匀功率分配达到信道容量，基矩阵的耦合宽度与耦合长度必须满足正则条件，并在码率趋近容量时趋于无穷。针对耦合宽度与耦合长度任意有限选取的基矩阵，我们提出一种新型功率分配策略——V形功率分配。V形功率分配将更多功率分配给基矩阵的外侧列以启动解码过程，而将较少功率分配给内侧列，形似字母V。我们证明，在大码长极限下，给定码率时V形功率分配较均匀功率分配能确保更宽信噪比范围内的成功解码。在有限码长场景中，仿真结果表明：仿照字母V形的功率分配可提升SC-SPARC的误码性能。