Joint source-channel coding using variable length codes

We address the problem of joint source-channel coding when variable-length codes are used for information transmission over a discrete memoryless channel. Data transmitted over the channel are interpreted as pairs (m k ,t k ), where m k is a message generated by the source and t k is a time instant when the transmission of the kth codeword begins. The decoder constructs an estimate of the transmitted sequence of pairs, and the kth decoding error is introduced as the event that the pair (m k ,t k ) does not belong to this sequence. We describe the maximum likelihood decoding algorithm and prove a lower bound on the exponent of the decoding error probability. For a subclass of discrete memoryless sources and discrete memoryless channels, this bound is asymptotically tight

Strategy for data transmission over binary channels with noiseless feedback and upper bound on the number of questions in searching with lies

A transmission strategy that allows the sender to deliver any of M messages to the receiver over a binary channel when at most e errors can occur is presented. The total number of bits required by the strategy differs from the known lower bound by 3e. This statement simultaneously gives a new upper bound on the number of questions in the process of searching with lies known as the "Ulam's game"

A new coding algorithm for trees

We construct a one-to-one mapping between binary vectors of length $n$ and preorder codewords of regular, ordered, oriented, rooted, binary trees having $N \approx n + 2$ log $n$ nodes. The mappings in both directions can be organized in such a way that complexities of all transformations are measured by linear functions of $n$. The approach is then completely extended to non-regular binary trees and partially extended to $D$-ary trees with $D > 2$