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

摘要

We consider the decoding of convolutional codes using an error trellis constructed based on a subma-trix of a given check matrix. In the proposed method, the syndrome-subsequence computed using the remaining submatrix is utilized as auxiliary information for decoding. Then the ML error path is correctly decoded using the degenerate error trellis. We also show that the decoding complexity of the proposed method is basically identical with that of the conventional one based on the original error trellis. Next, we apply the method to check matrices with monomial entries proposed by Tanner et al. By choosing any row of the check matrix as the submatrix for error-trellis construction, a 1-state error trellis is obtained. Noting the fact that a likelihood-concentration on the all-zero state and the states with many 0's occurs in the error trellis, we present a simplified decoding method based on a 1-state error trellis, from which decoding-complexity reduction is realized.%畳込み符号の検査行列の部分行列から構成されるエラートレリスを用いた復号法を捷案する．検査行列の残りの部分行列から計算されたシンドローム部分系列を復号の補助情報に用いれば，元の最尤エラーパスが正しく復号されることを示す．次に，この復号法をThnner等により提案されたLDPC畳込み符号の検査行列へ適用する．エラートレリスの構成に用いる部分行列として任意の“行”を選ぶと，成分が全てDの単項式なので，これらの単項式を全て掃き出すと状態数1のエラートレリスを構成できる．また，エラートレリスでは特定の状態に対し尤度の集中が起きている．この特徴に注目し，1状態エラートレリスに準最適復号法を適用して復号複雑度の低減を図る．