Vector Trellis Quantization for Noisy Channels

Abstract

The channel coding theorem of information theory indicates that if the rate of a binary sequence is less than the capacity of the channel over which the binary sequence is to be transmitted, then the source can be reproduced at the channel output with arbitrarily small error probability [1], [2]. Based on this, one can isolate the problem of channel coding from that of source coding. In other words, channel encoder, channel, and channel decoder may be considered as a noiseless link between the output of the source encoder and the input of source decoder, as long as source encoder’s output has a rate less than the capacity of the channel [3]. However, this separation is optimal only asymptotically, i.e., in the limit of arbitrarily complex overall encoders and decoders involving arbitrarily long blocklengths. In practice, where we encounter the curse of complexity and are forced to deal with finite blocklengths, such a separation results in a certain degree of sub-optimality.