Transmission errors and forward error correction in embedded Differential Pulse Code Modulation

We have derived formulas for the combined effects of quantization and transmission errors on the performance of embedded Differential Pulse Code Modulation (DPCM), a source code that can be used for variable-bit-rate speech transmission. Our analysis is more general and more precise than previous work on transmission errors in digital communication of analog signals. Special cases include conventional DPCM and Pulse Code Modulation (PCM). Our main result is a signal-to-noise ratio formula in which the effects of source characteristics (input signal, codec design parameters) and the effects of transmission characteristics (modulation, channel, forward error correction) are clearly distinguishable. We also present, in computationally convenient forms, specialized formulas that apply to uncoded transmission through a random-error channel, transmission through a slowly fading channel, and transmission with part or all of the DPCM signal protected by an error-correcting code. Numerical results show how channel coding can have different effects on conventional and embedded DPCM. They also show how the binary-number representation of quantizer outputs influences performance.