Comtech EF Data DMD-2050E - Manual (Page 93)

DMD2050E Universal Satellite Modem Theory of Operation
MN-DMD2050E Revision 2 3–51
C/N = C/N
o
– 10 log B [where B is bandwidth in Hz]
E
b
/N
o
= C/N
o
– 10 log R [where R is data rate in bits/sec]
= C/N + 10 log B – 10 log R
= C/N – 10 log (Spectral Efficiency)
E
b
/N
o
= 10 log (10 ((Co+No/No)/10) – 1) – 10 log (Spectral Efficiency)
[Spectral Efficiency is in bps / Hz]
3.12 TPC and Low Density Parity Check (LDPC) Coding
In the past few years there has been an unprecedented resurgence in interest in Forward Error
Correction (FEC) technology. The start of this new interest has its origins in the work done by
Claude Berrou
et al , and the 1993 landmark paper, Near Shannon Limit Error Correcting Coding
and Decoding – Turbo Codes . FEC is considered an essential component in all wireless and
satellite communications in order to reduce the power and bandwidth requirements for reliable
data transmission.
Claude Shannon, considered by many to be the father of modern communications theory, first
established the concept
of Channel Capacity in his 1948 paper A Mathematical Theory of
Communication . This places an absolute limit on how fast it is possible to transmit error-free data
within a channel of a given bandwidth, and with given noise conditions within that channel. He
concluded that it would only be possible to approach this limit through the use of source encoding
– what is familiar today as Forward Error Correction.
Shannon postulated that if it were possible to store every possible message in the receiver,
finding the stored message that most closely matched the incoming message would yield an
optimum decoding method. However, for all but the shortest bit sequences, the memory required
for this, and the time taken to perform the comparisons, makes this approach impractical. For all
practical purposes, the memory requirement and the decoding latency become infinite.
For many years, there were few advances in the quest to approach the Shannon Limit. The
Viterbi algorithm heralded a major step forward, followed in the early 1990s by the concatenation
of a Viterbi decoder with Reed-Solomon hard-decision block codes. It remained clear, however,
that the Shannon Limit was still an elusive target.
Berrou’ s work on Turbo Codes showed, through the use of an ingeniously simple approach
(multiple, or
iterative decoding passes) that it is possible to achieve performance close to the
Shannon Limit. Berrou’ s early work dealt exclusively with iteratively-decoded convolutional
codes (Turbo Convolutional Coding, or TCC), but in time the iterative approach was applied to a
particular class of block codes called Product Codes – hence Turbo Product Coding (TPC). TPC