Introduction - Comtech EF Data CDM-625A Installation And Operation Manual

CDM-625A Advanced Satellite Modem
Appendix B
B.7 TPC and Low Density Parity Check (LDPC) coding
B.7.1

Introduction

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
exhibits inherently low decoding latency compared with TCC, and so is considered much more
desirable for 2-way, interactive satellite communications applications.
In August 1999, Comtech became the first company in the world to offer satellite modems that
incorporate TPC. Since its inception, Comtech has continued to develop and refine its
implementation of TPC in its products, and now offers a comprehensive range of code rates
(from Rate 5/16 to Rate 0.95) and modulations (from BPSK to 16-QAM). However, in the past
few years, as part of the general interest in Turbo coding, a third class of Turbo coding has
emerged: Low Density Parity Check Codes (LDPC).
LDPC is more like TPC than TCC in that it is an iteratively-decoded block code. Gallager first
suggested this in 1962 but, at the time, the implementation complexity was considered to be
too great; for decades, it remained of purely academic interest. Further interest in LDPC was
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