Erasurekanava

Erasurekanava, or erasure channel, is a simple model used in information theory to study reliable communication when some transmitted symbols are lost. In a discrete memoryless erasure channel with input alphabet of size q, the channel outputs either the original symbol X with probability 1-p or an erasure symbol “?” with probability p. The receiver is made aware of which positions were erased, but not the original symbols in those positions.

In this model, the capacity, i.e., the maximum achievable information rate with arbitrarily low error, is C = (1-p) log2 q bits per channel use. For the binary erasure channel (q = 2), this reduces to C = 1 - p bits per use. The capacity-achieving input distribution is uniform over the input alphabet due to the channel’s symmetry.

Coding implications: Because an erasure provides no information about the transmitted symbol, decoding focuses on recovering the original data from the non-erased positions. Erasure codes, including Reed-Solomon (q-ary MDS codes), LDPC-based codes, and fountain codes, are designed to approach capacity by ensuring that any sufficiently large set of non-erased outputs yields the original data. In networks, the erasure channel is a common abstraction for packet loss, where whole packets may be dropped.

Variants and extensions include burst erasures, non-binary alphabets, and time-varying erasure probabilities. The erasure channel remains a foundational, tractable model for analyzing coding strategies and understanding the limits of reliable communication under symbol loss.