A System Approach to Quantization and Transmission Error

When designing a system to sample the output of an analog data source and to transmit the samples over a digital channel, the usual approach is to consider the errors introduced by quantization and transmission as separate problems. However, from a system viewpoint, a conflict arises. On the one hand, the quantization resolution can be improved by using all of the available positions in a data stream to carry information. Alternatively, the transmission accuracy can be improved if redundancy and error-correcting codes are introduced by converting some of the information positions into parity 1219 1220 T H E BELL SYSTEM TECHNICAL JOURNAL, M A Y - J U N E 1969 check positions. The problem then is to determine the proper allocation of the available symbols in order to reduce the average system error rather than concentrate exclusively on either the quantization problem or the transmission problem. We consider a data transmission system with uniform quantization. The average absolute error t h a t occurs between the analog source and the destination is used as the criterion of system performance. The criterion, termed the average system error (ASE) , is used to evaluate and compare the effectiveness of various systems. Some work has been done on the design of error-correcting codes which provide different amounts of protection for different positions within a code word. In Ref. 1, the general algebraic properties of these codes, referred to as unequal error protection codes, were investigated.