We face the following dilemma for designing low-density parity-check codes(LDPC) for quantum error correction. 1) The row weights of parity-check shouldbe large: The minimum distances are bounded above by the minimum row weights ofparity-check matrices of constituent classical codes. Small minimum distancetends to result in poor decoding performance at the error-floor region. 2) Therow weights of parity-check matrices should not be large: The sum-productdecoding performance at the water-fall region is degraded as the row weightincreases. Recently, Kudekar et al. showed spatially-coupled (SC) LDPC codesexhibit capacity-achieving performance for classical channels. SC LDPC codeshave both large row weight and capacity-achieving error-floor and water-fallperformance. In this paper, we design SC LDPC-CSS (Calderbank, Shor and Steane)codes for quantum error correction over the depolarizing channels.
展开▼
