# Symbol vs. Word (Digital Communication Theory)

So I'm trying to understand and link up the different chapters I've studied in a communications module. So here goes

I understand a Pulse Code Modulation System is made up of the following broad blocks

1. Analog Source goes to
2. Antialiasing Filter
3. Sampler
4. Quantizer
5. Binary Word Assignment
6. Line Coding
7. Sent through channel

Now I understand that in the Line Coding part, a pulse shaping filter is used. My confusion is that we usually refer to a small segment of bits as a symbol when dealing with the line coding part, but then what's the point of the word assignment (block 5).

What's the difference between a word and a symbol?

• Probably the difference between valid and invalid, my guess. Usually, the symbol space is a subset of the binary word space. Of course, I don't have a copy of the curriculum you have. So I can only guess.
– jonk
Commented May 12, 2018 at 21:17
• A symbol is a bit in the word. If you let them be square, then their bandwidth interferes with the adjacent pulses, creating inter symbol interference. (ISI). If the pulses have a sinc shape, their bandwidth is reduced in half, and it will avoid ISI. This is the role of the pulse shaping filter, belonging to the line coding block: it simply shapes the pulses (symbols). It can't shape them as a sinc (infinite bandwidth), but they can be approximated through a raised cosine forming filter. Commented May 13, 2018 at 7:29
• I simplified it a bit too much, I should have said that the symbol depends on the modulation, for example in 2-ASK you get two symbols per bit. But, from a simplistic POV, a symbol is corresponds to a bit (encoded in a particular way). From here, you continue to the pulse shaping filter. Commented May 13, 2018 at 7:44

A symbol is what is transmitted , received and detected and there are many different symbols for a bit, a sync word and perhaps others in different forms of communication.

When frequency compression is used such as QAM/QPSK there can be many bits per symbol or bits/Hz BW. In RZ baseband a symbol is a pulse that Returns to Zero if it is a "1" so the "symbol" is 1/2 bit also same for Manchester or Bi-Phase the symbols are twice the bit rate.

In PCM it is binary with 1 bit per symbol but it is also synchronous so there is a special unique sync word for frame synchronization so here the symbol is the Sync word or I guess it could be called a Binary Word Assignment. There may be other words for Forward Error Correction such as Hamming Codes. Each of these are also Symbols but used synchronized to the frame and used to improve symbol error rate , frame synchronization and thus resulting bit error rate (BER) and message error rate for a block of words.

So Sync words can also be "symbols" which express a certain pattern and may also satisfy other theoetical opitmization such as Correlation Function in case of low SNR and improvements on Sync Symbol detection with an auto-correlator.

Symbol definition in a general sense. Ref: Wiki

Symbols take the form of words, sounds, gestures, ideas or visual images and are used to convey other ideas and beliefs.

For example, a red octagon may be a symbol for "STOP",

... which is an english traffic word, as is each character and so is each bit and sync word in PCM.

However data words are not classified as symbols as they can be random data which may be assigned to specific meanings not generally defined as "symbols" in communication but perhaps values in channels such part of a DS1 Telephony data frame structure or diagnostic signalling S channel.

I wasn't satisfied with the way the comments turned out, so I decided I'll write down an answer, but leave the comments there, for shaming. Hopefully it'll be more clear.

The word is the binary number assigned for the quantized value, be it 4, 8, 16, etc bits long. The encoding alters the word, in effect, the consituent bits, in order to prepare them for transmission, usually over radio waves. Since a 1111 cannot be transmitted efficiently, different encodings exist. For example 2-ASK creates an oscillating pulse for every bit. Here's how a 0101 would look like (V(orig) is shifted for comparison):

This is what I meant that each symbol corresponds to a bit (in a rather convoluted way). The symbols are the bits that make the encoded signal. Here, you have two symbols per bit, each bit takes two alternating values. Further on, the pulse shaping may apply some oversampling (for higher transmitting frequency) while band-limitting the signal (to reduce the ISI). For example, here's the same 0101 shaped by a raised cosine with an oversampling of 8:

There are many types of modulations, to each its own. This was just a (visual) example.

A symbol is whatever we define it to be. Therefore it is important to have it properly defined for the particular application. A symbol could mean 1 bit of information - a low or a high. But for other systems, like in OFDM communications, an OFDM symbol could be a set of vectors, which in turn can be decoded to a relatively large set of binary bit information. So, when it comes to the word 'symbol' - it's important to define it for the particular application.