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assume that a sequence of symbols from the ensemble x introduced at the beginning of this chapter is compressed using
show that the elias code is not actually the best code for a prior distribution that expects very large integers do
describe an arithmetic coding algorithm to encode random bit strings of length n and weight k ie k ones and n -k zeroes
how many bits are needed to specify a selection of k objects from n objects n and k are assumed to be known and the
use a modified lempel-ziv algorithm in which as discussed on p120 the dictionary of prefixes is pruned by writing new
1 show that this modified lempel-ziv code is still not lsquocomplete that is there are binary strings that are not
is the standard binary representation for positive integers eg cb5 101 a uniquely decodeable codedesign a binary code
1 describe an arithmetic coding algorithm to generate random bit strings of length n with density f ie each bit has
compare the expected message length when an ascii file is compressed by the following three methodshuffman-with-header
a joint ensemble xy has the following joint distributionwhat is the joint entropy hx y what are the marginal entropies
the three cardsa one card is white on both faces one is black on both faces and one is white on one side and black on
estimate how many patterns in ay are recognizable as the character lsquo2 the aim of this problem is to try to
given twenty-four people in a room what is the probability that there are at least two people present who have the same
many texts draw figure 81 in the form of a venn diagram figure 82 discuss why this diagram is a misleading
a transatlantic cable contains n 20 indistinguishable electrical wires you have the job of figuring out which wire is
the technique of interleaving which allows bursts of errors to be treated as independent is widely used but is
for large integers k and n what fraction of all binary error correcting codes of length n and rate r kn are linear
design a code for the binary erasure channel and a decoding algorithm and evaluate their probability of error the
the birthday problem may be related to a coding scheme assume we wish to convey a message to an outsider identifying
poor mans noisy-channel coding theorem pretending that the union bound 1325 is accurate and using the average weight
1 what is the probability of block error of the n k hamming code to leading order when the code is used for a binary
some proteins produced in a cell have a regulatory role a regulatory protein controls the transcription of specific
if we wish to store s entries using a hash function whose output has m bits how many collisions should we expect to
show that the average time taken to find the required string in a raw list assuming that the original names were chosen
if we have checked the first few bits of xs with x and found them to be equal what is the probability that the correct