Upper bound for uniquely decodable codes in a binary input N-user adder channel

Shraga Bross, Ian F. Blake

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The binary input N-user added channel models a communication media accessed simultaneously by N users. In this model each user transmits binary sequences and the channel's output on each bit slot equals the sum of the corresponding N inputs. A uniquely decodable code for this channel is a set of N codes - a code for each of the N users - such that the receiver can determine all possible combinations of transmitted codewords from their sum. Van-Tilborg presented a method for determining an upper bound on the size of a uniquely decodable code for the two-user binary adder channel. He showed that for sufficiently large block length this combinatorial bound converges to the corresponding capacity region boundary. In the present work we use a similar method to derive an upper bound on the size of a uniquely decodable code for the binary input N-user adder channel. The new combinatorial bound is iterative - i.e., the bound for the (N - 1)-user case can be obtained by projecting the N-user bound on (N - 1) combinatorial variables and in particular it subsumes the two-user result. For sufficiently large block length the N-user bound converges to the capacity region boundary of the binary input N-user adder channels.

Original languageEnglish
Title of host publicationProceedings of the 1993 IEEE International Symposium on Information Theory
PublisherPubl by IEEE
Pages78
Number of pages1
ISBN (Print)0780308786
StatePublished - 1993
Externally publishedYes
EventProceedings of the 1993 IEEE International Symposium on Information Theory - San Antonio, TX, USA
Duration: 17 Jan 199322 Jan 1993

Publication series

NameProceedings of the 1993 IEEE International Symposium on Information Theory

Conference

ConferenceProceedings of the 1993 IEEE International Symposium on Information Theory
CitySan Antonio, TX, USA
Period17/01/9322/01/93

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