Digital Communications 1

5Binary to M-ary Coding and M-ary to Signal Coding: On-line Codes

5.1. Presentation and typology

A digital message, as a sequence of binary or M-ary elements called “information symbols”, is an abstract representation. To transmit this message, a physical quantity is associated with it in the form of an electrical signal (or optical signal for transmissions over optical fiber). This chapter describes the on-line codes used for baseband transmissions, as well as their most important properties.

The binary to M-ary transcoding and the M-ary to signal coding consists (see Figure 5.1) in:

• – a proper rule which allows one to associate with the binary sequence {b_n}, b_n ∈ [0,1] a sequence {a_n} where the symbols a_n belong to an alphabet of cardinal M > 2. This is called transcoding. Its essential purpose is to promote the operation that will follow (on-line code). This rule can be described in several ways: by a dictionary of codewords, by graph or state diagram;
• – an on-line coding which consists in constructing from each element a_n a waveform signal which occupies a time slice of at most T (with some exceptions) and which supports the symbol a. The signal thus formed at the output of the encoder is a so-called “baseband” signal. It is written:

[5.1]

where x(t) is a deterministic signal of a given pattern on the temporal interval [0, T[. A very common pattern for x(t) is that ...