Linear unequal error protection codes based on terminated convolutional codes

Abstract

Convolutional codes which are terminated by direct truncation (DT) and zero tail termination provide unequal error protection. When DT terminated convolutional codes are used to encode short messages, they have interesting error protection properties. Such codes match the significance of the output bits of common quantizers and therefore lead to a low mean square error (MSE) when they are used to encode quantizer outputs which are transmitted via a noisy digital communication system. A code construction method that allows adapting the code to the channel is introduced, which is based on time-varying convolutional codes. We can show by simulations that DT terminated convolutional codes lead to a lower MSE than standard block codes for all channel conditions. Furthermore, we develop an MSE approximation which is based on an upper bound on the error probability per information bit. By means of this MSE approximation, we compare the convolutional codes to linear unequal error protection code construction methods from the literature for code dimensions which are relevant in analog to digital conversion systems. In numerous situations, the DT terminated convolutional codes have the lowest MSE among all codes.