3.9 Randomizing and Encryption

Randomizing is not a channel code, but a technique that can be used in conjunction with almost any channel code. It is widely used in digital audio and video broadcasting and in a number of transmission formats. The randomizing system is arranged outside the channel coder . Figure 3.14 shows that, at the encoder, a pseudo-random sequence is added modulo-2 to the serial data. This process makes the signal spectrum in the channel more uniform, drastically reduces T _max and reduces DC content. At the receiver the transitions are converted back to a serial bitstream to which the same pseudo-random sequence is again added modulo-2. As a result, the random signal cancels itself out to leave only the serial data, provided that the two pseudo-random sequences are synchronized to bit accuracy.

Figure 3.14: Modulo-2 addition with a pseudo-random code removes unconstrained runs in real data. Identical process must be provided on replay.

Many channel codes, especially group codes, display pattern sensitivity because some waveforms are more sensitive to peak shift distortion than others. Pattern sensitivity is only a problem if a sustained series of sensitive symbols needs to be recorded. Randomizing ensures that this cannot happen because it breaks up any regularity or repetition in the data. The data randomizing is performed by using the exclusive-OR function of the data and a pseudo-random sequence as the input to the channel coder. On replay the same sequence is generated, synchronized to bit accuracy, and the exclusive-OR of the replay bitstream and the sequence is the original data.

Clearly, the sync pattern cannot be randomized, since this causes a situation where it is not possible to synchronize the sequence for replay until the sync pattern is read, but it is not possible to read the sync pattern until the sequence is synchronized!

In networks, the randomizing may be block based, since this matches the block structure of the transmission protocol. Where there is no obvious block structure, convolutional or endless randomizing can be used. In convolutional randomizing, the signal sent down the channel is the serial data waveform convolved with the impulse response of a digital filter. On reception the signal is deconvolved to restore the original data.

Convolutional randomizing is used in the serial digital interface (SDI) that carries 4:2:2 sampled video. Figure 3.15(a) shows that the filter is an infinite impulse response (IIR) filter having recursive paths from the output back to the input. As it is a one-bit filter its output cannot decay, and once excited, it runs indefinitely. Following the filter is a transition generator consisting of a one-bit delay and an exclusive-OR gate. An input 1 results in an output transition on the next clock edge. An input 0 results in no transition.

Figure 3.15: Convolutional randomizing encoder.

A result of the infinite impulse response of the filter is that frequent transitions are generated in the channel resulting in sufficient clock content for the phase-locked loop in the receiver.

Transitions are converted back to 1s by a differentiator in the receiver. This consists of a one-bit delay with an exclusive-OR gate comparing the input and the output. When a transition passes through the delay, the input and the output will be different and the gate outputs a 1 that enters the deconvolution circuit.

Figure 3.15(b) shows that in the deconvolution circuit a data bit is simply the exclusive-OR of a number of channel bits at a fixed spacing. The deconvolution is implemented with a shift register having the exclusive-OR gates connected in a reverse pattern to that in the encoder. The same effect as block randomizing is obtained, in that long runs are broken up and the DC content is reduced, but it has the advantage over block randomizing that no synchronizing is required to remove the randomizing, although it will still be necessary for deserialization. Clearly, the system will take a few clock periods to produce valid data after commencement of transmission, but this is no problem on a permanent wired connection where the transmission is continuous.

Where randomizing is used instead of a channel code, as in the serial digital interface, reliable operation depends on the statistics of the data. If the data to be transmitted have a certain combination of bits, the randomizing is defeated and the clock content is dramatically reduced. Such bit combinations are known as pathological sequences and may deliberately be generated for testing purposes. In video data, the probability of natural occurrence of pathological sequences is very small indeed, whereas in generic data it is not. This is why DVB-ASI cannot use this coding scheme.

In a randomized transmission, if the receiver is not able to re-create the pseudo-random sequence, the data cannot be decoded. This can be used as the basis for encryption in which only authorized users can decode transmitted data. In an encryption system, the goal is security whereas in a channel-coding system the goal is simplicity. Channel coders use pseudo-random sequences because these are economical to create using feedback shift registers. However, there are a limited number of pseudo-random sequences and it would be too easy to try them all until the correct one was found. Encryption systems use the same processes, but the key sequence that is added to the data at the encoder is truly random. This makes it much harder for unauthorized parties to access the data. Only a receiver in possession of the correct sequence can decode the channel signal. If the sequence is made long enough, the probability of stumbling across the sequence by trial and error can be made sufficiently small.