Recurrent Codes: Easily Mechanized, Burst-Correcting, Binary Codes

Hagelbarger, D. W.

doi:10.1002/j.1538-7305.1959.tb01584.x

Cited by 61 publications

(10 citation statements)

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“…However, there is no such guarantee in a GPON uplink because the signal power and the phase difference between packets vary in burst-mode reception from packet to packet. Burst-error correcting codes have been demonstrated for bursty channels [22][23][24][25][26], but these codes introduce complexity at the circuit level implementation. On the other hand, RS codes are relatively simple.…”

Section: Dynamic Burst-error Correctionmentioning

confidence: 99%

Performance analysis of burst-mode receivers with clock phase alignment and forward error correction for GPON

Shastri

Faucher²,

Kheder

et al. 2008

Analog Integr Circ Sig Process

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We experimentally demonstrate the performance analysis of burst-mode receivers (BMRx) in a 622 Mb/s 20-km gigabit-capable passive optical network (GPON) uplink. Our receiver features automatic phase acquisition using a clock phase aligner (CPA), and forward-error correction using (255, 239) Reed-Solomon (RS) codes. The BMRx provides instantaneous (0 preamble bit) phase acquisition and a packet-loss ratio (PLR) \ 10 -6 for any phase step (±2p rads) between consecutive packets, while also supporting more than 600 consecutive identical digits (CIDs). The receiver also accomplishes a 3-dB coding gain at a bit-error rate (BER) of 10 -10 . The CPA makes use of a phase picking algorithm and an oversampling clock-and-data recovery circuit operated at 29 the bit rate. The receiver meets the GPON physical media dependent layer specifications defined in the ITU-T recommendation G.984.2 standard. We investigate the PLR performance of the system and quantify it as a function of the phase step between consecutive packets, received signal power, CID immunity, and BER, while also assessing the tradeoffs in preamble length, power penalty, and pattern correlator error resistance. We also study the impact of mode-partition noise in the GPON uplink in terms of the effective PLR and BER coding gain performance of the system. In addition, we demonstrate how the CPA and the RS(255, 239) codes can be used in tandem for dynamic burst-error correction giving reliable BERs in bursty channels.

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Section: Dynamic Burst-error Correctionmentioning

confidence: 99%

Performance analysis of burst-mode receivers with clock phase alignment and forward error correction for GPON

Shastri

Faucher²,

Kheder

et al. 2008

Analog Integr Circ Sig Process

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“…Correcting burst erasures using convolutional codes has a long history starting in the late 1950's, and the achievable rates for convolutional codes that correct burst erasures have been discussed in numerous works including [11]- [14], but the optimality of the convolutional codes under delay constraints was not discussed until the work by Martinian and Sundberg [15] in 2004. In [15], streaming codes for the special case N = 1 are considered and the maximum achievable rate for convolutional codes over a channel that introduces only a single burst erasure (because N = 1)…”

Section: Related Workmentioning

confidence: 99%

Optimal Streaming Codes for Channels with Burst and Arbitrary Erasures

Fong

Khisti

et al. 2018

2018 IEEE International Symposium on Information Theory (ISIT)

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This paper considers transmitting a sequence of messages (a streaming source) over a packet erasure channel.In each time slot, the source constructs a packet based on the current and the previous messages and transmits the packet, which may be erased when the packet travels from the source to the destination. Every source message must be recovered perfectly at the destination subject to a fixed decoding delay. We assume that the channel loss model introduces either one burst erasure or multiple arbitrary erasures in any fixed-sized sliding window. Under this channel loss assumption, we fully characterize the maximum achievable rate by constructing streaming codes that achieve the optimal rate. In addition, our construction of optimal streaming codes implies the full characterization of the maximum achievable rate for convolutional codes with any given column distance, column span and decoding delay.Numerical results demonstrate that the optimal streaming codes outperform existing streaming codes of comparable complexity over some instances of the Gilbert-Elliott channel and the Fritchman channel. I. INTRODUCTIONLow-latency video conferencing has been a cornerstone for communication and collaboration for individuals and enterprises. The advent of 5G networks promises to make high-throughput at low-latency ubiquitous. This enables new applications such as high-quality video conferencing, virtual reality (VR) and Internet-of-things (IoT) applications including vehicle-to-vehicle communication and mission-critical machine-type communication [1]. At the core of these important applications is the need to reliably deliver packets with low latency. Packet losses at the physical layer and the network layer are inevitable, which may be caused by unreliable wireless links or congestion at network bottlenecks. In order to alleviate the effect of packet losses on applications that are run over the Internet, two main error control schemes have been implemented at the data link and transport layers: Automatic repeat request (ARQ) and forward error correction (FEC).For long-distance low-latency communication, it is not suitable to use ARQ schemes for error control because each retransmission incurs an extra round-trip delay. More specifically, correcting an erasure using ARQ results in a 3-way delay (forward + backward + forward), and this aggregate (3-way) delay including transmission, propagation and processing delays is required to be lower than 150 ms for interactive applications such as voice and video This paper was presented in part at 2018 IEEE International Symposium on Information Theory.

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“…An areal error burst of dimensions kT by kc, or (k~ X kc)-burst, may be defined as a pattern of errors in any subset of the digits in a rectangular area of length kr along the rows and length kc along the columns. Coding systems for the correction of k-bursts exist that are less redundant than those required for the correction of all error patterns of weight (r =< k. In particular, Abramson [4] has described a single-error-correcting and double-adjacent-error-correcting (SEc-DAEc) code, and Hagelbarger [5], Melas [6], and Meggitt [7] have presented codes for the correction of k-bursts for k => 2.…”

Section: Correlated Errorsmentioning

confidence: 98%

Two-Dimensional Parity Checking

Calingaert

1961

J. ACM

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Recurrent Codes: Easily Mechanized, Burst-Correcting, Binary Codes

Cited by 61 publications

References 1 publication

Performance analysis of burst-mode receivers with clock phase alignment and forward error correction for GPON

Performance analysis of burst-mode receivers with clock phase alignment and forward error correction for GPON

Optimal Streaming Codes for Channels with Burst and Arbitrary Erasures

Two-Dimensional Parity Checking

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