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BOUNDS ON PROBABILITY OF ERROR VERSUS
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amount of decoding average probability block length bound capacity region Cartesian product channel input digits coding capacity region complementary sets lemma conditional probability conditions of figure denote the set digits from alphabet discrete memoryless two-way error random variable expurgated bound feedback forbidden finite sets A,B,C forward direction forward reverse H M/M independent sources inner bound capacity inner bound region inner capacity bound integer log S-l lower bound memoryless two-way channel mutual information n-sequence random variable n+l)aa National Science Foundation oeveooe dioection one-way optimization outer capacity bound outer capacity region Pp(l probability measure probability of error proof r,r pair random coding bound rate pair R,R renaming the directions reverse direction sequential decoding sets A,B,C respectively Shannon shift register Similarly source rate pair sources with feedback sphere packing strong converse Theorem 3a.2a transmission upper bound variables over finite weak coding capacity weak converse weighting function X,Y,Z random variables