Error-Trellis State Complexity of LDPC Convolutional Codes Based on Circulant Matrices

摘要

QC符号を定義するパリティ検査行列別こ対し，行に関する巡回シフトを行ってH'と変形し，これからTanner等の方法に従ってH'(D)を構成すると，H′（D）で定義される畳込み符号のd_(free)は，元のH'で定義されるQC符号のd_(min)以上に保存されるが，一方でH'（D）に対応するエラートレリスの状態数は変化する．この事実に基づき，Hに施す行に関する巡回シフトを適当に制御することにより，誤り訂正能力を保持しつつ，変形後のH'（D）に対応するエラートレリスの状態数をかなり低減できることを示す．%Let H(D) be the parity-check matrix of an LDPC convolutional code corresponding to the parity-check matrix H of a quasi-cyclic (QC) code obtained using the method of Tanner et al. We see that the entries in H(D) are all monomials and several rows (columns) have monomial factors. Let us cyclically shift the rows of H. Then the parity-check matrix H'(D) corresponding to the modified matrix H' defines another convolutional code. However, its free distance is lower-bounded by the minimum distance of the original QC code. Also, each row (column) of H'(D) has a factor different from the one in H(D). Noting these facts, we show that the state-space complexity of the error-trellis associated with H'(D) can be significantly reduced by controlling the row shifts applied to H with the error-correcting capability being preserved.