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Reviewing Next-Generation Error Correction Codes

1/30/2013

DOUG LUNG |

At the Samsung booth at the CES International last month I saw a Korean Broadcasting System demonstration of 4K UHDTV transmitted over a 6 MHz channel using DVB-T2. Improved video compression techniques—MPEG-2, then H.264 and now HEVC—allow higher resolution at lower bit rates. Efficiently delivering these bits overthe- air requires digital coding to allow accurate recovery of the data stream in the presence of noise and interference.

**REVIEW OF DIGITAL CODES**

ATSC broadcasting uses Reed-
Solomon coding and trellis coding
to allow the 19.39 Mbps
data stream to be received with
a predicted signal-to-noise (SNR)
threshold as low as 15 dB SNR
in a 6 MHz channel. ATSC A/153
mobile DTV adds turbo codes to
drop the required SNR to as low
as 4 dB, but at a much lower data
rate. I explain how this works in
my article “Error Correction in
ATSC Mobile DTV” (RF Technology,
Nov. 3, 2010).

Since the ATSC standards were adopted, more powerful coding methods such as Low Density Parity Check (LDPC) and Bose-Chaudhuri Hocquenghem (BCH) have replaced Reed-Solomon coding and turbo codes as the preferred coding method for digital transmission. LDPC and BCH are used in the DVB-S2 and DVB-T2 standards.

Coding techniques can be
compared by seeing how
closely their performance
approaches the Shannon
limit. Fig. 1 is the cropped
lower-right portion of the
chart in Annex C of the
ATSC Final Report on ATSC
3.0 (*www.atsc.org*). It compares
the spectral efficiency
of existing and proposed
DTV transmission standards
in comparison with
the Shannon limit.

**
**

Fig. 1: Spectral efficiency of existing and proposed DTV transmission schemes. From “Final Report on ATSC 3.0 Next Generation Broadcast Television,” ATSC Planning Team 2, Advanced Television Systems Committee |

THE SHANNON LIMIT

The Shannon limit is named after its inventor, Claude Elwood Shannon, the mathematician who has been called “the father of information theory.” In 1948 he published the paper “A Mathematical Theory of Communications.” The paper showed how to calculate the maximum error-free data rate for a channel given its bandwidth and noise characteristics. Shannon called it “channel capacity,” but people soon began calling it the “Shannon limit.” It can be calculated using the formula:

Where W is the bandwidth in hertz, S is the average received signal power in watts, and N is the average noise power.

The solid blue line in Fig. 1 is the Shannon limit. The X axis is the carrier-to-noise ratio and the Y axis is the spectral efficiency in bits/second/hertz. You will notice that the green line is the one closest to the Shannon limit. This is DVB-T2, with QPSK, 16-QAM and 64-QAM modulation (left to right). 256-QAM is to the right in the full chart. DVB-T2, as noted, uses LDPC and BCH coding. The orange line represents LTE. The thin blue line with stars is A/53 VSB, but with LDPC coding. Notice how well it performs. The short red line is full channel A/153 mobile DTV, which uses turbo codes.

While it appears to be slightly better
than DVB-T2 LDPC coding at a 5 dB C/N,
the maximum data rate is extremely limited
and it is questionable whether this performance
is achievable with A/153 under real-
world conditions. Note that all of these
curves show *predicted* performance under
AWGN (Additive white Gaussian noise)
conditions.

**INTRODUCTION TO LPDC CODES**

The comparison chart shows the superior
performance of LDPC. LDPC codes
were first proposed by Robert G. Gallager
in his 1960 doctoral dissertation in the Department
of Electrical Engineering at M.I.T.
He expanded and revised the work in his
1963 paper “Low Density Parity Codes.”
However, the codes did not see practical
use until after the introduction of turbo
code in the mid 1990s.

The history of turbo codes is interesting. When Berrou and Glavieux presented turbo codes with simulation curves showing performance very close to the Shannon limit at the IEEE International Conference on Communications, many experts at the conference laughed at the claims and either did not attend the presentation or said the simulations were in error. Berrou and Glavieux, after all, were not mathematicians.

In his paper “Turbo Codes: Some Simple Ideas for Efficient Communications” Berrou writes, “The invention of turbo codes did not result from a linear limpid mathematical demonstration. It was the outcome of an empirical construction of a global coding/ decoding scheme, using existing bricks that had never been put together in this way before.”

Professor McEliece later said, “What
blew everyone away about turbo codes is
not just that they get so close to Shannon
capacity, but that they’re so easy. How could
we have overlooked them? Berrou and Glavieux
didn’t know the problem was supposed
to be hard, so they managed to find
a new way to go about it.” (from Prof. Angel
Lozano’s “Hall of Innovation” at *www.dtic.upf.edu/~alozano/innovation/*)

At the Samsung booth at the International CES last month, the Korean Broadcasting System demonstrated 4K UHDTV transmitted over a 6 MHz channel using DVB-T2. |

Today, the mathematicians appear to have won. LDPC codes, unlike turbo codes, have a decoding algorithm consisting of simple operations such as addition, comparison and table lookup. They can be parallelized in ways that make it easy to trade off throughput for complexity. Other researchers continued work on LDPC and produced new irregular codes that outperformed the best turbo codes. Indeed, given sufficient processing capability, it is now possible to produce LDPC codes that approach the Shannon limit within a few hundredths of a decibel!

After researching this article I’m beginning to believe that improvements in radio communication are going to depend as much on improved coding before modulation/ after demodulation as new RF transmission technology.

In future columns I’ll show how LDPC codes work (with as little math as possible) and show how they are used in today’s DVB-T2 and DVB-NGH standards.

*Comments and questions are welcome!
Email me at *dlung@transmitter.com*.*