A digital magnetic recording/reproducing apparatus that has an LVA detector, and that is able to maintain the coding rate as high as {fraction (8/9)} or more, and record at a higher density than in the prior art, wherein, in order that the data sequences up to the (2n−1)th best sequence (n>1) are obtained in the order of higher likelihood ratios, and that. the candidates of those data sequences can be produced, the LVA detector has provided therein a unit which replaces the likelihood ratio and path memory of the ith best sequence by those of the (2i−1)th best sequence when the contents of the (i−1)th path memory coincide with those of the ith path memory (i=2, 3, . . . , n) and the absolute value of the likelihood ratio difference between the (i−1)th best sequence and the (2i−1)th best sequence is smaller than a decision threshold, or a unit which initializes the likelihood ratio of the ith best sequence to be a constant difference value added to the likelihood ratio of the (i−1)th best sequence when the contents of the (i−1)th path memory and the ith (i=2, 3, . . . , n) path memory of the n candidates of data sequences are coincident.