Binary erasure channel erasure channel which shares many similar theoretical results with the binary erasure channel. The BEC is a "binary channel"; that is, it can transmit only one of two symbols (usually called 0 and 1). (A non-binary channel would be capable of transmitting more than two symbols, possibly even an infinite number of choices.) The channel is not perfect and sometimes the bit gets "erased"; that is, the bit gets scrambled so the receiver has no idea what the bit was. The BEC is, in a sense, error-free. Unlike the binary symmetric channel, when the receiver gets a bit, it is
Combinatorial number system "C"<nowiki>'</nowiki>, since they have the same largest part 9, but the next largest part 6 of "C" is less than the next largest part 7 of "C"<nowiki>'</nowiki>; the sequences compared lexicographically are (9,6,4,3,0) and (9,7,3,1,0). Another way to describe this ordering is view combinations as describing the "k" raised bits in the binary representation of a number, so that "C" = {"c"...,"c"} describes the number (this associates distinct numbers to "all" finite sets of natural numbers); then comparison of "k"-combinations can be done by comparing the associated binary numbers. In the example "C" and "C"<nowiki>'</nowiki> correspond to numbers 1001011001 =