Elements of information theory
Elements of information theory
Codes for Detecting and Correcting Unidirectional Errors
Codes for Detecting and Correcting Unidirectional Errors
Optimal Unidirectional Error Detecting/Correcting Codes
IEEE Transactions on Computers
Analysis of Plain and Diversity Combining Hybrid ARQ Protocols Over the -Ary Asymmetric Channel
IEEE Transactions on Information Theory
Feedback Codes Achieving the Capacity of the Z-Channel
IEEE Transactions on Information Theory
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In an unordered code no codeword is contained in any other codeword. Unordered codes are All Unidirectional Error Detecting (AUED) codes. In the binary case, it is well known that among all systematic codes with k information bits, Berger codes are optimal unordered codes with r = ⌈log2(k+1)⌉ check bits. This paper gives some new theory on variable length unordered codes and introduces a new class of systematic unordered codes with variable length check symbols. The average redundancy of these new codes is r ≈ (1/2) log2(πek/2) = (1/2) log2 k + 1.047, where k ∈ IN is the number of information bits. It is also shown that such codes are optimal in the class of systematic unordered codes with fixed length information symbols and variable length check symbols. The generalization to the non-binary case is also given.