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Coding in an asynchronous multiple-access channel. (English. Russian original) Zbl 0549.94017
Probl. Inf. Transm. 19, 184-191 (1983); translation from Probl. Peredachi Inf. 19, No. 3, 12-21 (1983).
The paper deals with the determination of the capacity region for a discrete memoryless channel with asynchronous multiple-access. This channel is specified by the transition probability matrix. Messages generated by two independent, memoryless sources are encoded by codes $$G_ 1$$ and $$G_ 2$$, respectively. The sources are stationary and the codes $$G_ 1$$ and $$G_ 2$$ have length n and rates $$R_ 1$$ and $$R_ 2$$. Using the mutual information, calculated on the basis of the transition probabilities and the message distribution, the author gives the converse encoding theorem for the asynchronous multiple-access channel (MAC). He proves that the capacity region is described by the convex closure of the set of the code rates.
Next, the author gives an upper bound for the decoding-error probability for trellis codes in the case of Viterbi’s decoding algorithm. In such a case the code sequences at the MAC input can be described by the trellis diagram. The author defines the set of all incorrect paths of length 1 in the trellis diagram. For these paths the probabilities of erroneous maximum-likelihood decoding of a block code are given.
Reviewer: J.Woźniak

##### MSC:
 94A24 Coding theorems (Shannon theory) 94B35 Decoding 62B10 Statistical aspects of information-theoretic topics 94A05 Communication theory