Proceedings ArticleDOI

Dirty paper coding using sign-bit shaping and LDPC codes

13 Jun 2010-pp 923-927

TL;DR: A lattice-based DPC scheme that provides good shaping and coding gains with moderate complexity at both the encoder and the decoder and a design for superposition coding that provides rates better than time-sharing over a Gaussian broadcast channel.

AbstractDirty paper coding (DPC) refers to methods for pre-subtraction of known interference at the transmitter of a multiuser communication system. There are numerous applications for DPC, including coding for broadcast channels. Recently, lattice-based coding techniques have provided several designs for DPC. In lattice-based DPC, there are two codes - a convolutional code that defines a lattice used for shaping and an error correction code used for channel coding. Several specific designs have been reported in the recent literature using convolutional and graph-based codes for capacity-approaching shaping and coding gains. In most of the reported designs, either the encoder works on a joint trellis of shaping and channel codes or the decoder requires iterations between the shaping and channel decoders. This results in high complexity of implementation. In this work, we present a lattice-based DPC scheme that provides good shaping and coding gains with moderate complexity at both the encoder and the decoder. We use a convolutional code for sign-bit shaping, and a low-density parity check (LDPC) code for channel coding. The crucial idea is the introduction of a one-codeword delay and careful parsing of the bits at the transmitter, which enables an LDPC decoder to be run first at the receiver. This provides gains without the need for iterations between the shaping and channel decoders. Simulation results confirm that at high rates the proposed DPC method performs close to capacity with moderate complexity. As an application of the proposed DPC method, we show a design for superposition coding that provides rates better than time-sharing over a Gaussian broadcast channel.

Introduction

• Situations where interference is known non-causally at the transmitter but not at the receiver model several useful multiuser communication scenarios.
• In [5], multilevel coding is used, and there are different codes for different bits of the symbols.
• In [8] and [9], shaping follows channel coding and the receiver performs iterations between the shaping and channel decoders.
• The rest of the paper is organized as follows.
• After a brief review of the lattice-based DPC coding method in Section II, the authors present the proposed DPC method in Section III.

II. LATTICE DIRTY PAPER CODES

• The transmit power is assumed to be upper-bounded by 1nE[|X|2] ≤ PX per symbol, and the interference power is denoted 1nE[|S|2] = PS per symbol.
• The noise variance per symbol is denoted PN .
• In [1], Costa shows that the capacity of the dirty paper channel is 12 log ( 1 + PXPN ) i.e. known interference can be canceled perfectly at the transmitter.
• The lattice transmission approach of [3] [4] is as follows.
• Note that the dither is assumed to be known at the transmitter and receiver (say, through the use of a common seed in a random number generator).

III. PROPOSED SCHEME

• The proposed scheme uses a convolutional code for signbit shaping [10] and low density parity check (LDPC) codes for channel coding.
• For M = 16, the constellation and mapping are shown in Fig.
• The mapping in Fig. 1 is suited for signbit shaping, since a flip of the most significant bit results in a significant change in symbol value for all possible 4-bit inputs.
• Also, the mapping is mostly Gray except for a few symbol transitions.
• As expected, larger values of M will result in larger shaping gains in their design, and the authors stick to the 16-PAM shown in Fig. 1 for illustration and simulation.

A. Encoder Structure

• The encoder structure for the proposed scheme is as shown in Fig.
• Note that the authors need the rate of the convolutional code to be 1−k′/s.
• Let the coset chosen by m′ be denoted C(m′).
• The sign-bit vector z is chosen from C(m′) so as to minimize the squared sum of the vector (v − αS) mod M , where α = PXPX+PN is the MMSE factor and S is the interference vector.
• In summary, the encoder structure achieves DPC shaping and LDPC coding with bit-interleaved modulation.

B. Decoder Structure

• The decoder for the proposed scheme is as shown in Fig.3.
• The decoded shaped bits are passed through a syndrome former to get message bits used for shaping.
• The LDPC decoder outputs k−k′ message bits and s bits of the sign bit vector of the previous block.
• The demapper function at the receiver has to calculate LLRs taking into account the modulo M operation at the encoder [4].
• Therefore, the received constellation AR is a replicated version of the M -PAM constellation A used at the transmitter (assuming that scaling factors have been corrected at the receiver).

IV. SIMULATION RESULTS

• A non-systematic convolutional code is used to avoid error propagation problems.
• The authors considered several candidate distributions originally designed for BPSK over AWGN, and chose the one that provided the best performance.
• The plot with interference did not change appreciably for all power levels of interference, and the authors have provided one plot for illustration.
• This shows that the authors are 1.46 dB away from ideal dirty paper channel capacity.
• The authors observed that trellis shaping with larger number of states results in a decrease in shaping loss in other simulations.

V. APPLICATION TO GAUSSIAN BROADCAST CHANNEL

• Here, User 2 is coded using DPC considering User 1 as interference.
• User 1 is shaped using sign-bit shaping and coded using an LDPC code over M -PAM.
• The demapper at Receiver 1 calculates LLR for the i-th bit in the j-th receiver symbol Y1j using the following formula.
• Comparison with the SNR needed for a single user capacity of 3 bits per channel use (which is 17.99 dB) shows that the total loss for both the users is about 2.4642dB.
• The authors see that the (3,3) rate point is clearly outside the time-sharing region.

VI. CONCLUSIONS

• The authors have proposed a method for designing lattice-based schemes for dirty paper coding using sign-bit shaping and LDPC codes.
• Simulation results show that the proposed design performs 1.46dB away from the dirty paper capacity for a block length of n = 40000 at the rate of 3 bits/channel use.
• This performance is comparable to other results in the literature.
• As discussed in this article, a novel method for combining shaping and coding results in good gains at lesser complexity in their design, when compared to other lattice-based strategies.
• As an application, the authors have designed a superposition coding scheme for Gaussian broadcast channels that is shown to perform better than timesharing through simulations.

Did you find this useful? Give us your feedback

Content maybe subject to copyright    Report

Dirty Paper Coding using Sign-bit Shaping and
LDPC Codes
Shilpa G, Andrew Thangaraj and Srikrishna Bhashyam
Dept of Electrical Engg
Chennai 600036, India
Email: andrew,skrishna@ee.iitm.ac.in
Abstract—Dirty paper coding (DPC) refers to methods for
pre-subtraction of known interference at the transmitter of a
multiuser communication system. There are numerous applica-
tions for DPC, including coding for broadcast channels. Recently,
lattice-based coding techniques have provided several designs for
DPC. In lattice-based DPC, there are two codes - a convolutional
code that deﬁnes a lattice used for shaping and an error
correction code used for channel coding. Several speciﬁc designs
have been reported in the recent literature using convolutional
and graph-based codes for capacity-approaching shaping and
coding gains. In most of the reported designs, either the encoder
works on a joint trellis of shaping and channel codes or the
decoder requires iterations between the shaping and channel
decoders. This results in high complexity of implementation. In
this work, we present a lattice-based DPC scheme that provides
good shaping and coding gains with moderate complexity at both
the encoder and the decoder. We use a convolutional code for
sign-bit shaping, and a low-density parity check (LDPC) code
for channel coding. The crucial idea is the introduction of a one-
codeword delay and careful parsing of the bits at the transmitter,
which enables an LDPC decoder to be run ﬁrst at the receiver.
This provides gains without the need for iterations between the
shaping and channel decoders. Simulation results conﬁrm that at
high rates the proposed DPC method performs close to capacity
with moderate complexity. As an application of the proposed DPC
method, we show a design for superposition coding that provides
rates better than time-sharing over a Gaussian broadcast channel.
I. INTRODUCTION
Situations where interference is known non-causally at
the transmitter but not at the receiver model several useful
multiuser communication scenarios. In [1], Costa introduced
and studied coding for such situations and called it “writing on
dirty paper”. Dirty paper coding (DPC) is now recognized as a
powerful notion central to approaching capacity on multiuser
channels.
Lattice-based ideas for DPC were suggested and shown to
be capacity-approaching in [2], [3]. Recently, many designs
of lattice-based DPC schemes have been proposed in [4]–[8].
Lattice-based schemes typically use cosets of a convolutional
code for lattice-quantizing or shaping to minimize the energy
of the difference of the coded symbols and the interfering
symbols. A part of the message bits is used to choose the
speciﬁc coset used in the minimization. In addition to the
shaping convolutional code, an error correction code needs
to be used to obtain coding gain and approach capacity.
The main source of complexity in lattice-based DPC designs
is combining shaping and coding encoders/decoders at the
transmitter/receiver. Simple concatenation schemes are not
applicable because of the following reasons - outer shaping
followed by inner coding results in unshaped parity symbols
that increase transmitted energy, while outer coding followed
by inner shaping results in a poor inner code that needs to be
iteratively decoded at the receiver with the outer code.
In [6], encoding is done on a combined trellis of the source
code (Turbo TCQ) and a channel code (Turbo TCM). At the
receiver, decoding is done for Turbo TCM followed by syn-
drome computation to recover message bits. The transmitter
is complex in [6] because of the use of the joint trellis. The
DPC method proposed in [7] is similar to that of [6]. In [5],
multilevel coding is used, and there are different codes for
different bits of the symbols. At the receiver, iterations have
to be performed between decoders for some of the channel
codes and the shaping decoder. In [8] and [9], shaping follows
channel coding and the receiver performs iterations between
the shaping and channel decoders.
In this work, we propose a lattice-based method that uses a
novel combination of a convolutional code for sign-bit shaping
and a low density parity check (LDPC) code for channel
coding. As shown in speciﬁc designs and simulations, the
method provides good shaping and coding gains at moderate
complexity. The main idea for reducing complexity at the
receiver is the introduction of a one-codeword delay at the
transmitter, and the shaping of symbols from current message
bits combined with parity bits from the previous codeword.
This enables the LDPC decoder to be run ﬁrst at the receiver
(with a one-codeword delay) without any need for iterations
with a shaping decoder. As an application, we use the proposed
DPC method to design codes for superposition coding in two-
user Gaussian broadcast channels. By simulations, we show
that rate points outside the time-sharing region are achieved.
The rest of the paper is organized as follows. After a brief
review of the lattice-based DPC coding method in Section
II, we present the proposed DPC method in Section III.
This is followed by description and simulation of speciﬁc
designs of DPC codes in Section IV. In Section V, design
of a superposition scheme using the proposed DPC method
is described and simulation results are presented. Concluding
remarks are made in Section VI.
ISIT 2010, Austin, Texas, U.S.A., June 13 - 18, 2010

5 citations

Cites background from "Dirty paper coding using sign-bit s..."

• ...With small groups (having only 2 or 3 users), dirty paper coding within each group is practically feasible and is equivalent to dirty paper coding for a MISO broadcast channel with small number of users [6], [7]....

[...]

Journal ArticleDOI
TL;DR: Numerical results show that causal knowledge of the interference provides more than 3 dB improvement in performance in certain scenarios over a scheme that does not use interference cancellation.
Abstract: In this paper, we present a practical application of dirty paper coding (DPC) for the Gaussian cognitive Z-interference channel. A two stage transmission scheme is proposed in which the cognitive transmitter first obtains the interference signal from the primary transmitter and then uses DPC to improve the performance of the cognitive link. Numerical results show that causal knowledge of the interference provides more than 3 dB improvement in performance in certain scenarios over a scheme that does not use interference cancellation. Results are also shown when the cognitive transmitter operates in both half-duplex and full-duplex modes.

3 citations

Cites methods from "Dirty paper coding using sign-bit s..."

• ...These DPC techniques typically use a combination of a vector quantizer and a capacity-approaching channel code like low density parity check (LDPC) code [14], [18], [19]....

[...]

References
More filters
Journal ArticleDOI
TL;DR: It is shown that the optimal transmitter adapts its signal to the state S rather than attempting to cancel it, which is also the capacity of a standard Gaussian channel with signal-to-noise power ratio P/N.
Abstract: A channel with output Y = X + S + Z is examined, The state S \sim N(0, QI) and the noise Z \sim N(0, NI) are multivariate Gaussian random variables ( I is the identity matrix.). The input X \in R^{n} satisfies the power constraint (l/n) \sum_{i=1}^{n}X_{i}^{2} \leq P . If S is unknown to both transmitter and receiver then the capacity is \frac{1}{2} \ln (1 + P/( N + Q)) nats per channel use. However, if the state S is known to the encoder, the capacity is shown to be C^{\ast} =\frac{1}{2} \ln (1 + P/N) , independent of Q . This is also the capacity of a standard Gaussian channel with signal-to-noise power ratio P/N . Therefore, the state S does not affect the capacity of the channel, even though S is unknown to the receiver. It is shown that the optimal transmitter adapts its signal to the state S rather than attempting to cancel it.

4,068 citations

Book
30 Nov 2008
TL;DR: The goal of this paper is to present in a comprehensive fashion the theory underlying bit-interleaved coded modulation, to provide tools for evaluating its performance, and to give guidelines for its design.
Abstract: Zehavi (1992) showed that the performance of coded modulation over a Rayleigh fading channel can be improved by bit-wise interleaving the encoder output and by using an appropriate soft-decision metric as an input to a Viterbi decoder. The goal of this paper is to present in a comprehensive fashion the theory underlying bit-interleaved coded modulation, to provide tools for evaluating its performance, and to give guidelines for its design.

2,098 citations

Journal ArticleDOI
TL;DR: The results provide an information-theoretic framework for the study of common communication problems such as precoding for intersymbol interference (ISI) channels and broadcast channels.
Abstract: We consider the generalized dirty-paper channel Y=X+S+N,E{X/sup 2/}/spl les/P/sub X/, where N is not necessarily Gaussian, and the interference S is known causally or noncausally to the transmitter. We derive worst case capacity formulas and strategies for "strong" or arbitrarily varying interference. In the causal side information (SI) case, we develop a capacity formula based on minimum noise entropy strategies. We then show that strategies associated with entropy-constrained quantizers provide lower and upper bounds on the capacity. At high signal-to-noise ratio (SNR) conditions, i.e., if N is weak relative to the power constraint P/sub X/, these bounds coincide, the optimum strategies take the form of scalar lattice quantizers, and the capacity loss due to not having S at the receiver is shown to be exactly the "shaping gain" 1/2log(2/spl pi/e/12)/spl ap/ 0.254 bit. We extend the schemes to obtain achievable rates at any SNR and to noncausal SI, by incorporating minimum mean-squared error (MMSE) scaling, and by using k-dimensional lattices. For Gaussian N, the capacity loss of this scheme is upper-bounded by 1/2log2/spl pi/eG(/spl Lambda/), where G(/spl Lambda/) is the normalized second moment of the lattice. With a proper choice of lattice, the loss goes to zero as the dimension k goes to infinity, in agreement with the results of Costa. These results provide an information-theoretic framework for the study of common communication problems such as precoding for intersymbol interference (ISI) channels and broadcast channels.

489 citations

"Dirty paper coding using sign-bit s..." refers background or methods in this paper

• ...In [3], a dirty paper coding (DPC) scheme based on lattice strategies was proposed and shown to achieve the capacity of the dirty paper channel....

[...]

• ...We follow [4] for a brief review of the transmitter and receiver structure in the lattice DPC method [3]....

[...]

• ...The lattice transmission approach of [3] [4] is as follows....

[...]

• ...Lattice-based ideas for DPC were suggested and shown to be capacity-approaching in [2], [3]....

[...]

Journal ArticleDOI
TL;DR: Trellis shaping, a method of selecting a minimum-weight sequence from an equivalence class of possible transmitted sequences by a search through the trellis diagram of a shaping convolutional code C/sub s/.
Abstract: The author discusses trellis shaping, a method of selecting a minimum-weight sequence from an equivalence class of possible transmitted sequences by a search through the trellis diagram of a shaping convolutional code C/sub s/. Shaping gains on the order of 1 dB may be obtained with simple four-state shaping codes and with moderate constellation expansion. The shaping gains obtained with more complicated codes approach the ultimate shaping gain of 1.53 dB. With a feedback-free syndrome-former for C/sub s/, transmitted data can be recovered without catastrophic error propagation. Constellation expansion and peak-to-average energy ratio may be effectively limited by peak constraints. With lattice-theoretic constellations, the shaping operation may be characterized as a decoding of an initial sequence in a channel trellis code by a minimum-distance decoder for a shaping trellis code based on the shaping convolutional code, and the set of possible transmitted sequences is then the set of code sequences in the channel trellis code that lie in the Voronoi region of the trellis shaping code. >

390 citations

"Dirty paper coding using sign-bit s..." refers methods in this paper

• ...A part of the message m′ = [m1 m2 · · ·mk′ ] with k′ < k bits is mapped to a coset leader of the convolutional code using an inverse syndrome former [10]....

[...]

• ...The proposed scheme uses a convolutional code for signbit shaping [10] and low density parity check (LDPC) codes for channel coding....

[...]

• ...The minimization in (6) is implemented using the Viterbi algorithm [10]....

[...]

Journal ArticleDOI
TL;DR: This work designs an end-to-end coding realization of a system materializing a significant portion of the promised gains and achieves an improvement of 2dB over the best scalar quantization scheme.
Abstract: The "writing on dirty paper"-channel model offers an information-theoretic framework for precoding techniques for canceling arbitrary interference known at the transmitter. It indicates that lossless precoding is theoretically possible at any signal-to-noise ratio (SNR), and thus dirty-paper coding may serve as a basic building block in both single-user and multiuser communication systems. We design an end-to-end coding realization of a system materializing a significant portion of the promised gains. We employ multidimensional quantization based on trellis shaping at the transmitter. Coset decoding is implemented at the receiver using "virtual bits." Combined with iterative decoding of capacity-approaching codes we achieve an improvement of 2dB over the best scalar quantization scheme. Code design is done using the EXIT chart technique.

325 citations

"Dirty paper coding using sign-bit s..." refers background or methods in this paper

• ...Recently, many designs of lattice-based DPC schemes have been proposed in [4]–[8]....

[...]

• ...Lower bounds on achievable rates for the above equivalent channel is shown in [4] to be equal to I (V;Y′) ≥ 1 2 log2 (1 + SNR) − 1 2 log2 (2πeG (Λ)) ....

[...]

• ...The demapper function at the receiver has to calculate LLRs taking into account the modulo M operation at the encoder [4]....

[...]

• ...The lattice transmission approach of [3] [4] is as follows....

[...]

• ...We follow [4] for a brief review of the transmitter and receiver structure in the lattice DPC method [3]....

[...]

Q1. What are the contributions in "Dirty paper coding using sign-bit shaping and ldpc codes" ?

In most of the reported designs, either the encoder works on a joint trellis of shaping and channel codes or the decoder requires iterations between the shaping and channel decoders. In this work, the authors present a lattice-based DPC scheme that provides good shaping and coding gains with moderate complexity at both the encoder and the decoder. This provides gains without the need for iterations between the shaping and channel decoders. As an application of the proposed DPC method, the authors show a design for superposition coding that provides rates better than time-sharing over a Gaussian broadcast channel.

Optimizing the LDPC code using genetic algorithms and asymmetric density evolution [ 12 ] along with joint optimization of shaping code and LDPC code using EXIT charts [ 8 ] are topics for future work.

The SNR for Receiver 1 is computed as 10 log10 ( PX1PX2+PN1) = 19.1791 dB. SinceDPC is done for User 2, the effective SNR at Receiver 2 is computed as 10 log10 ( PX2 PN2 ) = 19.4574 dB.

In a Gaussian dirty paper channel, the received symbolvector Y = [Y1 Y2 · · ·Yn] is modeled as Y = X + S + N,where X = [X1 X2 · · ·Xn] denotes the transmitted vector, S = [S1 S2 · · ·Sn] denotes the interfering vector assumed to be known non-causally at the transmitter and N denotes the additive Gaussian noise vector.

The bits that map to the i-th symbol are denoted zia2ia3i · · · ali; the sign-bit vector is denoted z = [z1 z2 · · · zs], and the authors define vectors aj = [aj1 aj2 · · · ajs] for 2 ≤ j ≤ l.

Simulation results show that the proposed design performs 1.46dB away from the dirty paper capacity for a block length of n = 40000 at the rate of 3 bits/channel use.

The granular gain G(Λ) = 22R/6Sx is computed from the simulations to be 1.282dB [4], where R = 3.5 is the rate before channel coding, and Sx is the transmit power (obtained through simulations).

Let m′′ = [z mk′+1 · · ·mk] be input to the systematic LDPC encoder to obtain the codeword E(m′′) = [m′′ pT ], where pT is the parity-bit vector for the T -th block.

The interfering vector S is used as an input in the encoding process and plays an important role to determine a suitable transmit vector X. A coding strategy for choosing X needs to overcome the imminent addition of S and protect the transmitted information from the addition of the noise N. Such coding strategies are called dirty paper coding (DPC) methods.

Because of the one-codeword delay, parity bits of the T + 1-th block and message plus shaped bits of the T -th block form a valid LDPC codeword.

1. The mapping in Fig. 1 is suited for signbit shaping, since a flip of the most significant bit results in a significant change in symbol value for all possible 4-bit inputs.

The transmit power is assumed to be upper-bounded by 1nE[|X|2] ≤ PX per symbol, and the interference power is denoted 1nE[|S|2] = PS per symbol.

In [1], Costa shows that the capacity of the dirty paper channel is 12 log ( 1 + PXPN ) i.e. known interference can be canceled perfectly at the transmitter.

The total transmit power, power for User 1 and power for User 2 required for a bit error rate of 10−5 (at both receivers) are estimated from the simulation and denoted P , Px1 and PX2 , respectively.

At the receiver, the authors approximate pi usinga Gaussian distribution with variance PS assuming that the distribution of M -PAM symbols is approximately Gaussian.

The authors use the proposed scheme for superposition coding in a two-user Gaussian broadcast channel Y1 = X + N1 and Y2 = X + N2 with PN1 > PN2 .

The number of replications r is chosen so that the average power of AR is approximately equal to the total average power PX + PS , and the bit mapping of the symbol a + jM (a ∈ A, 1 ≤ j ≤ r) is the same as that for a.

The s = nlog2M LLRs of the sign bits after a delay on one time step, and then−s output LLRs of the de-interleaver are given as the input to the LDPC decoder.