Some contributions to asymmetric error control codes
Bella Bose, Samir Elmougy · 2005
In some practical systems, most of the errors are of 1 → 0 type and 0 → 1 errors occur very rarely. In this thesis, first, the capacity of the asymmetric channel is derived. The capacity of the binary symmetric channel (BSC) and the Z-channel can be derived from this expression as special cases. Second, the error detecting capability of Bose-Lin codes beyond the maximum designed error detection capability are described. Third, a new class of a systematic t-unidirectional error detecting codes over Zm, m ≥ 2 is designed. These codes can detect 2 errors using r = 2 check bits and up to mr −2 + r − 2 errors using r > 2 check bits. Some upper bound on the maximum number of detectable errors when using r check bits are given. Finally, some analysis on the data throughput when using the following protocols over the m-ary Z-Channel, m ≥ 2 are derived: (1) ARQ protocols using t-Asymmetric Error Detecting (t-AED) codes. (2) ARQ protocols using All Asymmetric Error Detecting (AAED) codes. (3) Type-I Hybrid ARQ protocols using t-Asymmetric Error Correcting and All Asymmetric Error Detecting (t-EC|AAED) codes. (4) ARQ Protocols with diversity combining using t-Asymmetric Error Correcting and All Asymmetric Error Detecting (t-EC| AAED) codes. Finally, some open research problems are described.