Performance of different strategies for error detection and correction in arithmetic encoding

Lossless source encoding is occasionally used in some data compression applications. One of these encoding schemes is the arithmetic encoding. When data is to be transmitted via communication channel, noise and impurities imposed by the channel cause errors. To reduce the effect of errors, channel encoder is added prior to transmission through the channel. Channel encoder inserts some bits that help channel decoder at the receiver end to detect and correct errors. These added error detection and correction bits are redundancy that causes reduction in the compression ratio and hence an increase in data rate through the channel. The higher the detection and correction capability, the larger the added redundancy needed. Different approach for error detection and correction is used in this work. It is suitable for lossless data compression wherein errors are assumed to occur with low rate but causes very high propagation. That is, an error in one data symbol causes all the following symbols to be in error with high probability. This was shown to be the case in arithmetic encoding and Lemple-Ziv algorithms for data compression. With this approach, redundancy in a form of a marker, is added to the data before it is compressed by the source encoder. The decoder examine the data for existence of errors and correct them. Different approaches for redundancy marker is examined and compared. As a measure for comparison, we used misdetection by testing one or more marker location, as well as miscortrection. These performance measures are calculated analytically and by computer simulation. The results are also compared to those obtained with channel encoding such as Hamming codes. We found that our approach performs as well as channel encoder. However, while Hamming codes results in an erroneous data when more than one error occurs, this approach gives a clear indication for this situation