# Forward error correction

In telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding[1][2] is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is the sender encodes the message in a redundant way by using an error-correcting code (ECC).

The redundancy allows the receiver to detect a limited number of errors that may occur anywhere in the message, and often to correct these errors without re-transmission. FEC gives the receiver the ability to correct errors without needing a reverse channel to request re-transmission of data, but at the cost of a fixed, higher forward channel bandwidth. FEC is therefore applied in situations where re-transmissions are costly or impossible, such as one-way communication links and when transmitting to multiple receivers in multicast. For example, in the case of a satellite orbiting around Uranus, a re-transmission because of decoding errors can create a delay of 5 hours. FEC information is usually added to mass storage (magnetic, optical and solid state/flash based) devices to enable recovery of corrupted data, is widely used in modems, is used on systems where the primary memory is ECC memory and in broadcast situations, where the receiver does not have capabilities to request retransmission or doing so would induce significant latency.

FEC processing in a receiver may be applied to a digital bit stream or in the demodulation of a digitally modulated carrier. For the latter, FEC is an integral part of the initial analog-to-digital conversion in the receiver. The Viterbi decoder implements a soft-decision algorithm to demodulate digital data from an analog signal corrupted by noise. Many FEC coders can also generate a bit-error rate (BER) signal which can be used as feedback to fine-tune the analog receiving electronics.

The maximum fractions of errors or of missing bits that can be corrected is determined by the design of the ECC, so different forward error correcting codes are suitable for different conditions. In general, a stronger code induces more redundancy that needs to be transmitted using the available bandwidth, which reduces the effective bit-rate while improving the received effective signal-to-noise ratio. The noisy-channel coding theorem of Claude Shannon answers the question of how much bandwidth is left for data communication while using the most efficient code that turns the decoding error probability to zero. This establishes bounds on the theoretical maximum information transfer rate of a channel with some given base noise level. His proof is not constructive, and hence gives no insight of how to build a capacity achieving code. However, after years of research, some advanced FEC systems like polar code[2] come very close to the theoretical maximum.

## References

1. ^ Charles Wang; Dean Sklar; Diana Johnson (Winter 2001–2002). "Forward Error-Correction Coding". Crosslink. The Aerospace Corporation. 3 (1). How Forward Error-Correcting Codes Work
2. ^ a b Maunder, Robert (2016). "Overview of Channel Coding".
10G-EPON

The 10 Gbit/s Ethernet Passive Optical Network standard, better known as 10G-EPON allows computer network connections over telecommunication provider infrastructure. The standard supports two configurations: symmetric, operating at 10 Gbit/s data rate in both directions, and asymmetric, operating at 10 Gbit/s in the downstream (provider to customer) direction and 1 Gbit/s in the upstream direction. It was ratified as IEEE 802.3av standard in 2009. EPON is a type of passive optical network, which is a point-to-multipoint network using passive fiber optic splitters rather than powered devices for fan-out from hub to customers.

Code rate

In telecommunication and information theory, the code rate (or information rate) of a forward error correction code is the proportion of the data-stream that is useful (non-redundant). That is, if the code rate is ${\displaystyle k/n}$ for every ${\displaystyle k}$ bits of useful information, the coder generates a total of ${\displaystyle n}$ bits of data, of which ${\displaystyle n-k}$ are redundant.

If ${\displaystyle R}$ is the gross bitrate or data signalling rate (inclusive of redundant error coding), the net bitrate (the useful bit rate exclusive of error-correction codes) is ${\displaystyle \leq R\cdot k/n}$.

For example: The code rate of a convolutional code will typically be ${\displaystyle 1/2}$, ${\displaystyle 2/3}$, ${\displaystyle 3/4}$, ${\displaystyle 5/6}$, ${\displaystyle 7/8}$, etc., corresponding to one redundant bit inserted after every single, second, third, etc., bit. The code rate of the octet oriented Reed Solomon block code denoted RS(204,188) is 188/204, meaning that ${\displaystyle 204-188=16}$ redundant octets (or bytes) are added to each block of 188 octets of useful information.

A few error correction codes do not have a fixed code rate—rateless erasure codes.

Note that bit/s is a more widespread unit of measurement for the information rate, implying that it is synonymous with net bit rate or useful bit rate exclusive of error-correction codes.

Digital Satellite Service

Digital Satellite System is the initialism expansion of the DSS digital satellite television transmission system used by DirecTV. Only when digital transmission was introduced did direct broadcast satellite (DBS) television become popular in North America, which has led to both DBS and DSS being used interchangeably to refer to all three commonplace digital transmission formats - DSS, DVB-S and 4DTV. Analog DBS services, however, existed prior to DirecTV and were still operational in continental Europe until April 2012.At the time of DirecTV's launch in 1994, the DVB-S digital satellite system in use in the majority of the world had not yet been standardised, the Thomson developed DSS system was used instead.

While functionally similar in DVB-S - MPEG 2 video, MPEG-1 Layer II or AC3 audio, QPSK modulation, and identical error correction (Reed-Solomon coding and Viterbi forward error correction), the transport stream and information tables are entirely different from those of DVB. Also unlike DVB, all DSS receivers are proprietary DirecTV reception units.

DirecTV is now using a modified version of DVB-S2, the latest version of the DVB-S protocol, for HDTV services off the SPACEWAY-1, SPACEWAY-2, DirecTV-10 and DirecTV-11 satellites; however, huge numbers of DSS encoded channels still remain. The ACM modulation scheme used by DirecTV prevents regular DVB-S2 demodulators from receiving the signal although the data carried are regular MPEG-4 transport streams.

Diversity scheme

In telecommunications, a diversity scheme refers to a method for improving the reliability of a message signal by using two or more communication channels with different characteristics. Diversity is mainly used in radio communication and is a common technique for combatting fading and co-channel interference and avoiding error bursts. It is based on the fact that individual channels experience different levels of fading and interference. Multiple versions of the same signal may be transmitted and/or received and combined in the receiver. Alternatively, a redundant forward error correction code may be added and different parts of the message transmitted over different channels. Diversity techniques may exploit the multipath propagation, resulting in a diversity gain, often measured in decibels.

E-VSB

E-VSB or Enhanced VSB is an optional enhancement to the original ATSC Standards that use the 8VSB modulation system used for transmission of digital television. It is intended for improving reception where signals are weaker, including fringe reception areas, and on portable devices such as handheld televisions or mobile phones. It does not cause problems to older receivers, but they cannot take advantage of its features. E-VSB was approved by the ATSC committee in 2004. However, it has been implemented by few stations or manufacturers.For mobile applications, ATSC suffers significant signal degradation caused by the Doppler effect. Additionally, low-power handheld receivers are usually equipped with smaller antennas. These have a poor signal-to-noise ratio, which is disruptive to digital signals. The E-VSB standard provides for Reed-Solomon forward error correction to alleviate the data corruption caused by these issues.

Additionally, the standard can use either the MPEG-4 AVC or VC-1 video codecs. As these codecs have higher video compression than the original MPEG-2, they require less bandwidth.

As 8VSB lacks both link adaptation and hierarchical modulation of DVB, which would allow the SDTV part of an HDTV signal (or the LDTV part of SDTV) to be received even in fringe reception areas where signal strength is low, E-VSB yields a similar benefit. However, E-VSB places a significant processing overhead on the receiver, as well as a significant transmission overhead on the broadcaster's total bitrate. These are not a problem with DVB-H.

A-VSB is a different and, as of July 2008, unapproved addition to ATSC, which is also designed to send programming to mobile devices, and to allow for single-frequency networks. It is one of several proposals for ATSC-M/H, the as-yet undecided standard for mobile broadcasting via ATSC.

Erasure code

In coding theory, an erasure code is a forward error correction (FEC) code under the assumption of bit erasures (rather than bit errors), which transforms a message of k symbols into a longer message (code word) with n symbols such that the original message can be recovered from a subset of the n symbols. The fraction r = k/n is called the code rate. The fraction k’/k, where k’ denotes the number of symbols required for recovery, is called reception efficiency.

Errored second

In telecommunications and data communication systems, an errored second is an interval of a second during which any error whatsoever has occurred, regardless of whether that error was a single bit error, or a complete loss of communication for that entire second; the type of error is not important for the purpose of counting errored seconds.

In communication systems with very low uncorrected bit error rates, such as modern fiber optic transmission systems, or systems with higher low-level error rates that are corrected using large amounts of forward error correction, errored seconds are often a better measure of the effective user-visible error rate than the raw bit error rate.

For many modern packet-switched communication systems, even a single uncorrected bit error is enough to cause the loss of a data packet by causing its CRC check to fail; whether that packet loss was caused by a single bit error or a hundred-bit-long error burst is irrelevant.

For systems using large amounts of forward error correction, the reverse applies; a single low-level bit error will almost never occur, since any small errors will almost always be corrected, but any error sufficiently large to cause the forward error correction to fail will almost always result in a large burst error.

More specialist and precise definitions of errored seconds exist in standards such as the T1 and DS1 transport systems.

FX.25 Forward Error Correction

FX.25 is a protocol extension to the AX.25 Link Layer Protocol. FX.25 provides a Forward Error Correction (FEC) capability while maintaining legacy compatibility with non-FEC equipment. FX.25 was created by the Stensat Group in 2005, and was presented as a technical paper at the 2006 TAPR Digital Communications Conference in Tucson, AZ.

Hybrid automatic repeat request

Hybrid automatic repeat request (hybrid ARQ or HARQ) is a combination of high-rate forward error-correcting coding and ARQ error-control. In standard ARQ, redundant bits are added to data to be transmitted using an error-detecting (ED) code such as a cyclic redundancy check (CRC). Receivers detecting a corrupted message will request a new message from the sender. In Hybrid ARQ, the original data is encoded with a forward error correction (FEC) code, and the parity bits are either immediately sent along with the message or only transmitted upon request when a receiver detects an erroneous message. The ED code may be omitted when a code is used that can perform both forward error correction (FEC) in addition to error detection, such as a Reed–Solomon code. The FEC code is chosen to correct an expected subset of all errors that may occur, while the ARQ method is used as a fall-back to correct errors that are uncorrectable using only the redundancy sent in the initial transmission. As a result, hybrid ARQ performs better than ordinary ARQ in poor signal conditions, but in its simplest form this comes at the expense of significantly lower throughput in good signal conditions. There is typically a signal quality cross-over point below which simple hybrid ARQ is better, and above which basic ARQ is better.

IPoDWDM

IP over DWDM (IPoDWDM) is a technology used in telecommunications networks to integrate IP Routers and Switches in the OTN (Optical Transport Network).

A true IPoDWDM solution is implemented only when the IP Routers and Switches support ITU-T G.709. In this way IP devices can monitor the optical path and implement the transport functionality as FEC (Forward Error Correction) specified by ITU-T G.709/Y.1331 or Super FEC functionality defined in ITU-T G.975.1.

MPEG-H

MPEG-H is a group of international standards under development by the ISO/IEC Moving Picture Experts Group (MPEG). It has various "parts" – each of which can be considered a separate standard. These include a media transport protocol standard, a video compression standard, an audio compression standard, a digital file format container standard, three reference software packages, three conformance testing standards, and related technologies and technical reports. The group of standards is formally known as ISO/IEC 23008 – High efficiency coding and media delivery in heterogeneous environments. Development of the standards began around 2010, and the first fully approved standard in the group was published in 2013. Most of the standards in the group have been revised or amended several times to add additional extended features since their first edition.

MPEG-H consists of the following parts:

Part 1: MPEG Media Transport (MMT) – a media streaming format similar to the Real-time Transport Protocol that is adaptable to different networks

Part 2: High Efficiency Video Coding (HEVC, jointly developed with the ITU-T Video Coding Experts Group and also published as ITU-T H.265) – a video compression standard that doubles the data compression ratio compared to H.264/MPEG-4 AVC

Part 3: 3D Audio – an audio compression standard for 3D audio that can support many loudspeakers

Part 4: MMT Reference and Conformance Software (not yet published)

Part 5: Reference Software for High Efficiency Video Coding (also published as ITU-T H.265.2)

Part 6: 3D Audio Reference Software

Part 7: MMT Conformance (not yet published)

Part 8: Conformance Specification for HEVC (also published as ITU-T H.265.1)

Part 9: 3D Audio Conformance Testing

Part 10: MPEG Media Transport Forward Error Correction Codes

Part 11: MPEG Media Transport Composition Information

Part 12: Image File Format – a.k.a. High Efficiency Image File Format (HEIF), based on the ISO base media file format

Part 13: MPEG Media Transport Implementation Guidelines (a technical report rather than a standard)

Part 14: Conversion and Coding Practices for HDR/WCG Y′CbCr 4:2:0 Video with PQ Transfer Characteristics (a technical report also published as ITU-T H-series supplement 15)

Part 15: Signalling, backward compatibility and display adaptation for HDR/WCG video (a technical report also published as ITU-T H-series supplement 18)

Packet erasure channel

The packet erasure channel is a communication channel model where sequential packets are either received or lost (at a known location). This channel model is closely related to the binary erasure channel.

An erasure code can be used for forward error correction on such a channel.

RTVideo

RTVideo is Microsoft's default video codec for Office Communications Server 2007 and the Microsoft Office Communicator 2007 client.

It is a Microsoft proprietary implementation of the VC-1 codec for real-time transmission purposes.

Microsoft extensions to VC-1 are based on cached frame and SP-frame.

Also it includes system-level enhancements for recovery of packet loss on IP networks - forward error correction and error concealment.

SITOR

SITOR (SImplex Teletype Over Radio) is a system for transmitting text messages. Although it uses the same frequency-shift keying (FSK) modulation used by regular radioteletype (RTTY), SITOR uses error detection, redundancy, and/or retransmission to improve reliability.

There are two SITOR modes:

SITOR-A is used for point to point links. SITOR-A uses automatic repeat request (ARQ) to gain reliability. If the receiver detects an error, it requests a retransmission.

SITOR-B is used for broadcast links. SITOR-B transmits each character in a message twice to gain reliability. If the receiver detects an error in the first character, it uses the copy. If both characters are garbled, the receiver won't know what was sent.

SITOR-B by definition uses forward error correction (FEC), versus ARQ for SITOR-A.SITOR sends 7-bit characters as a bit stream at 100 baud (which, in this case, is 100 bits per second, 10 milliseconds per bit, or 70 milliseconds per character).

The bitstream is FSK modulated with a 170 Hz frequency shift. The high frequency is a mark, and the low frequency is a space.

SMPTE 2022

SMPTE 2022 is a standard from the Society of Motion Picture and Television Engineers (SMPTE) that describes how to send digital video over an IP network. Video formats supported include MPEG-2 and serial digital interface The standard was introduced in 2007.The standard is published in seven parts.

ST 2022-1:2007 - Forward Error Correction for Real-Time Video/Audio Transport Over IP Networks

ST 2022-2:2007 - Unidirectional Transport of Constant Bit Rate MPEG-2 Transport Streams on IP Networks

ST 2022-3:2010 - Unidirectional Transport of Variable Bit Rate MPEG-2 Transport Streams on IP Networks

ST 2022-4:2011 - Unidirectional Transport of Non-Piecewise Constant Variable Bit Rate MPEG-2 Streams on IP Networks

ST 2022-5:2013 - Forward Error Correction for Transport of High Bit Rate Media Signals over IP Networks (HBRMT)

ST 2022-6:2012 - Transport of High Bit Rate Media Signals over IP Networks (HBRMT)

ST 2022-7:2013 - Seamless Protection Switching of SMPTE ST 2022 IP DatagramsSMPTE 2022 is an important technology enabling the transition of broadcast systems to IP networking.

SerDes Framer Interface

SerDes Framer Interface is a standard for telecommunications abbreviated as SFI. Variants include:

SFI-4 or SerDes Framer Interface Level 4, a standardized Electrical Interface by the Optical Internetworking Forum (OIF) for connecting a synchronous optical networking (SONET) framer component to an optical serializer/deserializer (SerDes) for Optical Carrier transmission rate OC-192 interfaces at about 10 Gigabits per second.

SFI-5 or SerDes Framer Interface Level 5, a standardized Electrical Interface by the OIF for connecting a SONET Framer component to an optical SerDes for OC-768, about 40 Gbit/s. Electrically, it consists of 16 pairs of SerDes channels each running at 3.125 Gbit/s which gives an aggregate bandwidth of 50 Gbit/s accommodating up to 25% of Forward Error Correction

Turbo code

In information theory, turbo codes (originally in French Turbocodes) are a class of high-performance forward error correction (FEC) codes developed around 1990–91 (but first published in 1993), which were the first practical codes to closely approach the channel capacity, a theoretical maximum for the code rate at which reliable communication is still possible given a specific noise level. Turbo codes are used in 3G/4G mobile communications (e.g., in UMTS and LTE) and in (deep space) satellite communications as well as other applications where designers seek to achieve reliable information transfer over bandwidth- or latency-constrained communication links in the presence of data-corrupting noise. Turbo codes compete with LDPC codes, which provide similar performance.

The name "turbo code" arose from the feedback loop used during normal turbo code decoding, which was analogized to the exhaust feedback used for engine turbocharging. Hagenauer has argued the term turbo code is a misnomer since there is no feedback involved in the encoding process.

Windows Media Services

Windows Media Services (WMS) is a streaming media server from Microsoft that allows an administrator to generate streaming media (audio/video). Only Windows Media, JPEG, and MP3 formats are supported. WMS is the successor of NetShow Services.In addition to streaming, WMS also has the ability to cache and record streams, enforce authentication, impose various connection limits, restrict access, use multiple protocols, generate usage statistics, and apply forward error correction (FEC). It can also handle a high number of concurrent connections making it suitable for content providers. Streams can also be distributed between servers as part of a distribution network where each server ultimately feeds a different network/audience. Both unicast and multicast streams are supported (multicast streams also use a proprietary and partially encrypted Windows Media Station (*.nsc) file for use by a player.) Typically, Windows Media Player is used to decode and watch/listen to the streams, but other players are also capable of playing unencrypted Windows Media content (Microsoft Silverlight, VLC, MPlayer, etc.)

64-bit versions of Windows Media Services are also available for increased scalability. The Scalable Networking Pack for Windows Server 2003 adds support for network acceleration and hardware-based offloading, which boosts Windows Media server performance. The newest version, Windows Media Services 2008, for Windows Server 2008, includes a built-in WMS Cache/Proxy plug-in which can be used to configure a Windows Media server either as a cache/proxy server or as a reverse proxy server so that it can provide caching and proxy support to other Windows Media servers. Microsoft claims that these offloading technologies nearly double the scalability, making Windows Media Services, according to the claim, the industry's most powerful streaming media server.Windows Media Services 2008 is no longer included with the setup files for the Windows Server 2008 operating system, but is available as a free download. It is also not supported on Windows Server 2012, having been replaced with IIS Media Services.

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