# Presentation: 813869

## Design of a New Multiuser Line CodeA. Al-Sammak* * EEE Department, U. of Bahrain, Isa Town, Bahrain R. L. Kirlin**# and P.F. Driessen** ** ECE Department, U. of Victoria, Victoria, B.C., Canadapresented by R. L. Kirlin

## Objectives

**Find a code that allows multiple users to simultaneous access the same data channel**
**Maximize  efficiency, trading off ****	**
**number of users **
**number of symbols per user**
**number of bits per symbol **
** ****Compare to other schemes**** **

## Results

**May use as a single user line code**** ****by partitioning data stream into “users’” symbols.**
**Produces higher rates than QAM and TDM because higher dimensional signal space is used **
**Up to 4.4 bits/baud for 22 users, 2 symbols/user, and 5 bits/symbol**

## Methodology

**Similar to collaborative coding multiple access (CCMA) techniques**
**Permit simultaneous transmission by multiple users over a common binary adder channel or over a shared radio channel **
**Combined users’ symbol codes must be uniquely decodeable**

## Example coding process

**1**
**0**
**1**

**U = 3 users’ source symbols, **
**M = 2 symbols/user, assigned to **
**2-bit words, **_**m **_**(only for cc)**

**Lookup table combines **_**m**_**i**

**1 3**

**B = 2-time-slot data word  **_**V**_** transmitted**

**0 1**
**0 1**
**1 1**

## Problems 

** ****Alternately, given U users, what is the minimum number B of bits that is required.**
** ****How do we decode the M user symbols associated with each V?**

**Problems **

## EXAMPLE

**Needs only M****U**** = 2****4**** = 16 points from the N****v**** = (U+1)****B**** = 25  possible combinations **_**V**_** in the 2-dimensional space, i.e. from the grid of size (U+1)****B**** =  5****2**** ******** 25 points  ...**

**EXAMPLE**

## U = 4, M = 2, B = 2 

**Example showing size and use of signal space; **
**U = 4, M = 2, B = 2**** **

## We may use “QAM-like” constellations, as shown for the  U = 4 users  B = 2 time slots

## Alternate constellation diagram for U=4 , B=2, M = 2 symbols/user illustrating both direct transmit level coding and PAM transmission.

**Alternate constellation diagram for U=4 , B=2, M = 2 symbols/user illustrating both direct transmit level coding and PAM transmission.**

## Table 1: Constellations for 4-user code

-        Constellation         user symbols        Direct Tx            Symmetric
-         assignment              u1  u2  u3  u4             levels	             PAM
- 	1		0000		2 1		0  –1
- 	2		0001		0 1		-2 –1
- 	3		0010		1 0		-1 –2
- 	4		0011		0 0		-2 –2
- 	5		0100		3 2		 1   0
- 	6		0101		4 1		 2 –1
- 	7		0110		3 0		 1 –2
- 	8		0111		4 0		 2 –2
- 	9		1000		1 2		 -1  0
- 	10		1001		0 3		 -2  1
- 	11		1010		1 4		 -1  2
- 	12		1011		0 4		 -2  2
- 	13		1100		2 3		  0  1
- 	14		1101		4 3		  2  1
- 	15		1110		3 4		  1  2
- 	16		1111		4 4		  2  2

## Implications

** ****The number of dimensions in the signal space is B.**
** ****The number of possible unique values (levels)   of the sum vectors **_**V**_**  is N****Vmax**** =  (U+1)****B****.**
** ****The maximum number of unique symbols available to all users is M****max****  = 2****B.**
-  **The maximum number N****w**** of symbol combinations is M****max**** ****U**.
** ****Because the actual number N****w****  words used must be less than or equal to N****Vmax**** , we have the constraint:**
**	****	****N****w ****= M****U ******** N****Vmax**** = (U+1)****B**

## A most important point :

**We can use the constraint two ways: **
**either**
**1)  For fixed U and B we can select an M small enough that M****U**** ******** (U+1)****B****  **
**or **
**2) F****or a fixed M and U we may increase B so that M****U ******** (U+1)****B****. ****  **

##  Information Rate is defined as 

**R = log****2  ****M * (U/B)****	**
**user information bits / time-slot****	****	**
** ****Code Efficiency is defined as the symbol combinations used by the U users divided by the number of symbols available given B-bit symbols, **
**	******** ****= M****U****/(U+1)****B   ******** 1****	****	****	****	**

## Slide 15

## Slide 16

## Slide 17

## Slide 18

## Slide 19

## Conclusions

** ****The code may be used as a single user line code**** ****by partitioning data stream into blocks of U “users’” symbols.**
** ****U users’ simultaneous source symbols are encoded by lookup table according to the design, and decoded similarly.**
** ****It produces higher bits/baud or bits/dimension than QAM and TDM because a higher dimensional signal space is used (B bits / symbol).**

##  Maximum M , symbols/user and maximum number of users U, have been tabulated for most realistic cases when other parameters are fixed.

**Up to 4.4 bits/baud (bits/time slot) results with U = 22 users, M = 2 symbols/user, and B = 5 bits/symbol. **
** ****Design objectives have been achieved **