FFT-Based BP Decoding of General LDPC Codes Over Abelian Groups

Goupil, Alban; Colas, Maxime; Gellé, Guillaume; Declercq, David

doi:10.1109/tcomm.2007.894089

Cited by 47 publications

(36 citation statements)

References 14 publications

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“…On the other hand, for the transform F, it is not required that the indices of the elementsw form a field, it is sufficient that they form an Abelian group with respect to the additive operation (for a more detailed discussion on general LDPC codes, we recommend [26]). For this reason, the transform can still be performed in the same way as for scalar non-binary codes, but now on the additive group of F K q instead of F q .…”

Section: B Check Node Processingmentioning

confidence: 99%

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Joint decoding of multiple non-binary LDPC codewords

Pfletschinger¹

2014

2014 IEEE International Conference on Communications Workshops (ICC)

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We develop a belief-propagation (BP) decoder for the joint decoding of multiple codewords which belong to the same non-binary LDPC code. Decoding is based on soft information in form of joint channel-posterior probabilities of all codeword symbols. We extend the BP algorithm for q-ary LDPC codes such that the FFT-based check node processing is preserved and the complexity remains manageable. This joint decoding is useful in settings in which multiple codewords are transmitted in a non-orthogonal way over the same channel, including multipleaccess with packet collisions, physical-layer network coding and multi-resolution broadcasting. We show in an example that joint decoding can be far superior to separate decoding. I. INTRODUCTIONWe consider a joint decoder for multiple codewords of a non-binary LDPC code: different messages are encoded with a q-ary LDPC code and transmitted over a multiple-access channel (MAC) in a non-orthogonal way. The received signal hence depends on various codewords and separate decoding is generally suboptimum. This situation occurs e.g. in the following application areas:• Physical-layer network coding. While two-way relaying is the most obvious example [1]-[4], the considered setting also applies to the multi-way relay channel [5] and to compute-and-forward relaying [6]. • Slotted ALOHA and uncoordinated multiple-access schemes which take full advantage of the received signal and side information for collision resolution [7]-[10]. • Multi-resolution broadcast [11], [12], which transmits multiple data streams to users with different channel qualities or receiver capabilities. In this paper, we extend previous work on the joint decoding of binary LDPC [2], [4] or convolutional codes [13] to non-binary LDPC codes and do not restrict our attention to physicallayer network coding but rather focus on the details of the belief propagation (BP) algorithm for efficient joint decoding of multiple messages. Non-binary LDPC codes have shown significant benefits in channels which cannot be decomposed into binary subchannels without incurring a significant loss in achievable rates, e.g. for MIMO and for higher-order modulation [14], [15]. They have also been proposed for space communications since they outperform their binary counterparts in particular for short to moderate blocklength [16]. Since coding in higher-order Galois fields is imperative in many applications of random linear network coding [17], [18], applying the same field order for channel coding facilitates the integration of both approaches.

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Section: B Check Node Processingmentioning

confidence: 99%

“…An excellent description of the BP algorithm for nonbinary LDPC codes and protograph-based code design can be found in [16]. A very general description of generalizations of LDPC codes which allow FFT-based BP decoding and an application to the MAC has been given in [25], [26].…”

mentioning

confidence: 99%

Joint decoding of multiple non-binary LDPC codewords

Pfletschinger¹

2014

2014 IEEE International Conference on Communications Workshops (ICC)

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“…For both the presented classes of turbo and IRA codes, decoding can be efficiently implemented via FHTs [12], [13] with complexity O(q log q). In fact the messages exchanged by the iterative decoder along the edges of the graph are probability mass function (PMF) vectors with q elements.…”

Section: Short Ldpc/turbo Codes: Code Structurementioning

confidence: 99%

Codes on high-order fields for the CCSDS next generation uplink

Liva

Cola

Chiani

2012

2012 6th Advanced Satellite Multimedia Systems Conference (ASMS) and 12th Signal Processing for Space Communications Workshop (

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Recently, short binary and non-binary iterativelydecodable codes have been proposed within the Next Generation Uplink (NGU) working group (WG) of the Consultative Committee for Space Data Systems (CCSDS). The NGU WG targets the design of an enhanced uplink mainly for telecommand with the aim of updating the current uplink standard that employs a short (63, 56) BCH code to protect the telecommand messages. The proposed non-binary turbo/LDPC codes attain large coding gains over the standardized BCH codes, but also over their binary turbo/LDPC counterparts (up to 1.5 dB of coding gain for information blocks of 64 bits). This paper overviews the proposed non-binary code construction, illustrating the potential of nonbinary turbo/LDPC codes in the short block length regime. The impact of the proposed solution at system level is investigated, together with its integration in the CCSDS protocol stack.

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“…We do not have enough space in this paper to present in details the BP equations, or its reduced compexity versions, but the reader can refer to [4], [3], [2] for complete details.…”

Section: B Decoders For Non-binary Ldpc Codesmentioning

confidence: 99%

Non-Binary LDPC Codes Defined Over the General Linear Group: Finite Length Design and Practical Implementation Issues

Chen

Poulliat

Declercq

et al. 2009

VTC Spring 2009 - IEEE 69th Vehicular Technology Conference

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Abstract-Non-binary LDPC codes are now recognized as a potential competitor to binary coded solutions, especially when the codeword length is small or moderate. More and more works are reported with good performance/complexity tradeoffs, which make non-binary solutions interesting for practical applications, such as 4G-wireless systems or DVB-like systems.In this paper, we show that proposing non-binary LDPC codes build on finite fields is actually a limitation, both from performance and implementation aspects. By considering nonbinary codes on the general linear group, we show in particular that one can obtain a slight performance improvement compared to Galois field codes, with reasonable additional cost in the hardware implementation. The performance gain is quite small, but comes at a slight extra decoding cost, and is obtained by proper generalization of the code optimization techniques that are standard for non-binary LDPC codes on fields.

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FFT-Based BP Decoding of General LDPC Codes Over Abelian Groups

Cited by 47 publications

References 14 publications

Joint decoding of multiple non-binary LDPC codewords

Joint decoding of multiple non-binary LDPC codewords

Codes on high-order fields for the CCSDS next generation uplink

Non-Binary LDPC Codes Defined Over the General Linear Group: Finite Length Design and Practical Implementation Issues

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