interleaves

Interleave is the process of merging two or more sequences by alternating elements while preserving the internal order of each sequence. The resulting sequence contains all elements in the same relative order as they appeared in their source sequences.

In combinatorics, interleavings of two sequences of lengths m and n are the distinct sequences formed by merging while preserving order within each original sequence. The number of such interleavings is given by the binomial coefficient (m+n choose m) (equivalently (m+n choose n)). For more than two sequences, the concept extends to multi-way interleavings, counted by a multinomial coefficient.

In computing and communications, interleaving is used to mitigate burst errors by redistributing consecutive symbols across time or space. Block interleavers and convolutional interleavers are common examples. In memory systems, memory interleaving distributes addresses across multiple memory banks to increase parallelism and bandwidth, reducing latency and contention. Interleaving also describes data arrangements in storage systems, such as RAID layouts, and in multimedia, where color or audio/video samples are interleaved to enable smooth playback or transmission.

The term can also be used more broadly to refer to any scheme that alternates elements from different sources while preserving the internal order of each source. Interleaving is related but distinct from general permutation, which imposes no constraint on the relative order of elements from the original sequences.