NON - UNIFORM SIGNALING OVER BAND - LIMITED CHANNELS : A Multirate Signal Processing Approach

It is well known that if the communication channel is bandlimited to W Hz one can transmit at most 2W independent symbols per second. Generalized sampling theorems, nevertheless, do not restrict such a signaling to be uniform [1], [2], [3]. That is, it is theoretically possible to distribute the data symbols non-uniformly in time as long as the average signaling rate does not exceed 2W. Since the average baud rate remains the same, non-uniform signaling techniques are rarely used in normal communication scenarios. Recently, based on the observation that almost all of the public telephone network is digital, it has been proposed that 56 kb/s transmission is theoretically possible over voice band channels [7]. The proposed signaling is a nonuniform one which makes it possible to receive independent data symbols using available 8 kHz PCM samplers while the average baud rate is kept limited to 7 kbaud (W=3500 Hz). In this report, inspired by the results given in [4], a general frame work for non-uniform signaling over band limited channels is proposed. The analysis tool here is “multirate signal processing theory” using which it will be shown that when the channel is sampled with a rate higher than the Nyquist rate, M out of L output samples are allowed to be linearly independent as long as MF L W S / ≤ 2 . It is interesting to note that any subset of M samples in a frame of length L will work (which seems to be in contrast with the results claimed in [8].)