1. CT-474: Satellite Communications
Yash Vasavada
Autumn 2016
DA-IICT
Lecture 5
Modulation and Coding
17th August 2016

2. Review and Preview Preview of this lecture:
We will look at the process of modulation/demodulation and coding/decoding
Review of the prior lecture: relationships between some key design parameters:
Power 𝑃∝ 𝐴 2 and Energy per symbol 𝐸 𝑆 =𝑃× 𝑇 𝑆 : 𝑃 𝐸 𝑆 = 𝑅 𝑆
Energy per information bit 𝐸 𝑏 and Energy per symbol 𝐸 𝑆 : 𝐸 𝑆 = 𝑟 log 2 𝑘 𝐸 𝑏
Bit Rate 𝑅 𝑏 , Symbol Rate 𝑅 𝑆 , and Bandwidth 𝐵: 𝑅 𝑆 = 𝑅 𝑏 / 𝑟 log 2 𝑘 ; 𝐵= 1+𝛼 𝑅 𝑆
Noise power 𝑃 𝑁 = 𝑁 0 𝐵
SNR 𝑃 𝑆 𝑃 𝑁 = 𝐶 𝑁 and Per-symbol SNR 𝐸 𝑆 / 𝑁 0 : 𝐶 𝑁 = 1+𝛼 −1 𝐸 𝑆 𝑁 0 ; 𝐸 𝑆 𝑁 0 =𝑟 log 2 𝑘 𝐸 𝑏 𝑁 0

3. SNR and Bit Error Rate B A
Bit Error Rate or BER characterizes the performance of the receiver: 𝐵𝐸𝑅 = 𝑁 𝑒 𝑁 = 𝑁 𝑒 𝑁 𝑠 + 𝑁 𝑒
Here, 𝑁, 𝑁 𝑆 and 𝑁 𝑒 refer to the total number of transmitted bits, number of bits successfully received and number of bits in error
BER is categorized as follows:
Uncoded or raw BER: error rate without the error control coding; evaluated at point A
Coded BER is evaluated after channel decoder, at point B
A simplified block diagram of communication receiver B A

4. Operation of the Demodulator
Received symbol, because it is affected by the noise, can take a value that is significantly different from the transmitted symbol
Demodulator uses “decision regions”: if the received signal falls within the decision region corresponding to a transmitted symbol, say, 𝑠 𝑘 , it is assumed that that symbol 𝑠 𝑘 was transmitted
Decision region for 𝑠 𝑘 is a set of all points which are closer to 𝑠 𝑘 compared to 𝑠 𝑚 , 𝑚≠𝑘
With this rule, the detected symbol is not guaranteed to be correct, but it is guaranteed in AWGN channel to be the most likely symbol to have been transmitted
Demodulator makes an error if the additive noise is large enough to push the received signal outside of the decision region for 𝑠 𝑘
Probability of this error in demodulated bit is a function of the energy separation between the symbols, and the noise spectral density 𝑁 0 . For modulation constellations that are centered at origin, this is simply a function of per-bit SNR, or the ratio 𝐸 𝑆 / 𝑁 0

5. SNR and Bit Error Rate
Bit Error Rate for BPSK and QPSK is given by the following Q-function
𝑃 𝑏 =𝑄 𝐸 𝑆 𝑁 0

6. SNR and Bit Error Rate
Effect of error control coding is to reduce the required 𝐸 𝑏 / 𝑁 0 to achieve the same bit error rate
This directly allows a power saving
However, this power saving is achieved at the cost of an increased bandwidth consumption, since, as noted earlier, the bit rate 𝑅 𝑏 has to be inflated to 𝑅 𝑏 /𝑟 given code rate 0≤𝑟<1
Note that the occupied bandwidth 𝐵= 1+𝛼 𝑅 𝑏 𝑟 log 2 𝑘
Thus, we have traded power with the bandwidth. This trade-off is expanded upon next
Uncoded Performance
Potential performance of LDPC R = ½ BPSK/QPSK
Coding Gain

7. SNR and Bit Error Rate: Recent Advancement in Channel Encoding/Decoding
Conventional channel coded utilized either block codes such as Reed-Solomon or BCH codes, or Convolutional codes, or a concatenation of the two. In 1990’s, two new codes, LDPC and Turbo codes, improved upon the coding technology. Specifically, as the packet length of LDPC and Turbo codes increases…
The frame error rate (FER) of the encoded packet reduces
This is opposite of the behavior of the conventional codes, whose FER typically degrades with increasing packet size
However, since the packet length N has to be made large for LDPC or Turbo codes, each instance of packet error carries an increased consequence
The FER curves start exhibiting a cliff
This is in contrast to the waterfall-shaped FER performance curves for the conventional code
The LDPC/Turbo FER cliff can be made more vertical by increasing the decoder complexity (# of iterations)
No such complexity-performance trade typically exists for the conventional codes
Thus, with LDPC/Turbo codes, for large N values, only the cliff-point Es/No (or threshold) needs to be budgeted for. The channel becomes nearly error-free above the threshold Es/No
This is unlike the convolutional code for which Es/No has to be tied to a specific FER number
A side consequence: if Es/No drops below LDPC/Turbo threshold, the performance may severely degrades

8. SNR and Bit Error Rate: Recent Advancement in Channel Encoding/Decoding
Observation: AWGN channel turns into a nearly on-off channel dictated by Es/No threshold
Error rate falls off a cliff above the threshold; near zero errors above the threshold, near certainty of the error below the threshold
No need (ideally) to specify a packet error requirement; in reality a performance floor not seen here is likely to surface; performance cannot be improved beyond some very low packet error rate
Assumes a long length packet (64800 bits) [2]; shorter length packets may incur about 1 dB penalty as seen in comparison with the previous and the next slides

9. Power and Bandwidth Tradeoff
System designer’s objective: achieve the highest data rate possible
System constraints: limited available power and limited available bandwidth
Maximum possible data rate 𝑅 𝑏 that can be achieved given the power and bandwidth constraint is bounded by the following well-known equation by Claude Shannon that sets the channel capacity 𝐶
Assumes that the only impairment introduced by the transmission channel is the Additive White Gaussian- distributed Noise.
Such a channel is accordingly called the AWGN channel, and the following formula is known as the capacity of the AWGN channel
𝑅 𝑏 ≤𝐶=𝐵× log 𝑃 𝑆 𝑃 𝑁
bits per second