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Assume you have been hired to design a communication signaling system.
There are 8 users all transmitting their data to a common receiver. The
users are not coordinated with each other. Each user tries to transit data
to the receiver when the data is available. Each user’s data is composed of
packets. Each packet has a header followed by the encoded data. The header
contains information required by the receiver to make sure the data is processed
properly. The header itself also has an error correction code applied.
You can assume each user will start the transmission of a packet sometime
between 0 and 128 seconds where the start time is uniformly distributed between
0 and L seconds where L is such that L plus the packet time is 128
seconds (this assures that the end of a packet transmission will always occur
on or before the 128 second boundary marker). Each user will only transmit
one packet per 128 second interval.
The header is composed of 16 information bits. An (n, k) binary BCH code
is applied. More information about this code will be supplied in class.
1
The data is composed of one or more codewords. Each group of 8 information
bits is mapped to an 8-bit symbol for Reed-Solomon (RS) coding.
The RS code is an (n, k) code. This code will be discussed in class.
The encoded header combined with the encoded data make up a packet.
Each user’s packet is the same length.
At the receiver if two or more packets collide then all the data in each of
the affected packets is considered lost. Furthermore, if there is one or more
uncorrectable errors in the header then all the data in the corresponding
packet is lost. Also, if any uncorrectable errors occur in the RS codewords
then all the data in that codeword is lost. You can assume that the transmit
time from each user to the receiver is the same. Your task is to design the
packet lengths and coding structure.
You may assume an operating point of E/N0 = 6.5 dB, where E/N0 is
the energy available per bit (coded or uncoded). Each bit time is 1 msec.
Each bit is transmitted using BPSK modulation.
Part 1.
Design the system so that the expected throughput for each user is maximized.
Part 2.
Design the system to maximize the throughput such that each user’s information
in a packet is received and decoded successfully at least 95% of the time.
In the Summary section include the following information:
Part 1:
The BCH header is an (n,k) code (specify n and k).
The RS code is an (n,k) code (specify n and k).
The packet length is x seconds (specify x).
There is/are x RS codewords per packet (specify x).
The expected throughput for each user is x information bps (specify x).
2
Part 2:
The BCH header is an (n,k) code (specify n and k).
The RS code is an (n,k) code (specify n and k).
The packet length is x seconds (specify x).
There is/are x RS codewords per packet (specify x).
The throughput for each user to assure 95% reliability is x information bps
(specify x).