A multi-channel CRC register

High-speed parallel CRC circuits

“…Previous research [2], [3], [4], [5], [6], [8], [11], [12], [21], has focused on the cases where l ≤ m. In this paper, we provide a derivation and hardware structure for the case that l > m. This derivation can be easily modified for the other two cases, namely, l = m and l < m. Beginning with…”

“…Unlike the previously published matrix formations that begin from a state-space definition of the LFSR [11] or the LFSR inspection method [2], we start by recalling the earlier definition of the binary polynomial T (i) (x) in (4). Then, we introduce a matrix multiplication for representing the scalar T (i) (x) as the product of the row vector x 1×l = x 0 · · · x l−1 and the column vector…”

“…Different parallel hardware circuits and software algorithms that perform the CRC computation have been the subject of a substantial amount of research effort, e.g., see [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12] and [13], [14], [15], [16], [17], [18] for hardware and software deployments, respectively.…”

“…In this paper, we refer to l as the degree of parallelism. Shortly after [19], the author of [2] applied this technique to the CRC LFSR, and subsequently published a parallel CRC circuit. Many other works have since used this approach to obtain parallel CRC circuits, some examples include [5], [14], [20], [21], and [22].…”

“…In addition to the LFSR observation method, i.e., [2], [19], other methods for obtaining parallel CRC circuits have been proposed. In [3], a recursive approach based on state-space techniques is used to obtain a parallel implementation.…”