Peyman Razaghi

Bilayer Low-Density Parity-Check Codes for Decode-and-Forward in Relay Channels

This paper describes an efficient implementation of binning for decode-and-forward (DF) in relay channels using low-density parity-check (LDPC) codes. Bilayer LDPC codes are devised to approach the theoretically promised rate of the DF relaying strategy by incorporating relay-generated parity bits in specially designed bilayer graphical code structures. While conventional LDPC codes are sensitively tuned to operate efficiently at a certain channel parameter, the proposed bilayer LDPC codes are capable of working at two different channel parameters and two different rates: that at the relay and at the destination. To analyze the performance of bilayer LDPC codes, bilayer density evolution is devised as an extension of the standard density evolution algorithm. Based on bilayer density evolution, a design methodology is developed for the bilayer codes in which the degree distribution is iteratively improved using linear programming. Further, in order to approach to the theoretical DF rate for a wide range of channel parameters, this paper proposes two different forms of bilayer codes: the bilayer-expurgated and bilayer-lengthened codes. It is demonstrated that the rate of a properly designed bilayer LDPC code can closely approach the theoretical DF limit. Finally, it is shown that a generalized version of the proposed bilayer code construction is applicable to relay networks with multiple relays.

Capacity of a Class of Modulo-Sum Relay Channels

This paper characterizes the capacity of a class of modular additive noise relay channels, in which the relay observes a corrupted version of the noise and has a separate channel to the destination. The capacity is shown to be strictly below the cut-set bound in general and achievable using a quantize-and-forward strategy at the relay. This result confirms a previous conjecture on the capacity of channels with rate-limited side information at the receiver for this particular class of modulo-sum channels. This paper also considers a more general setting in which the relay is capable of conveying noncausal rate-limited side information about the noise to both the transmitter and the receiver. The capacity is characterized for the case where the channel is binary symmetric with a crossover probability 1/2. In this case, the rates available for conveying side information to the transmitter and to the receiver can be traded with each other arbitrarily-the capacity is a function of the sum of the two rates.

Parity Forwarding For Multiple-Relay Networks

This paper proposes a relaying strategy for networks with multiple relays where each relay forwards parities of decoded codewords. This parity-forwarding scheme can be thought of as a generalization of Cover and El Gamals well-known decode-and-forward strategy for the classic three-terminal relay channel to networks with multiple relays. As compared to previous multiple-relay decode-and-forward strategies, the parity-forwarding scheme is more flexible and can achieve a higher rate. The proposed strategy can be easily applied to networks with complex topologies. We show that relay networks can be degraded in more than one way, and parity-forwarding is capacity achieving for a new form of degraded relay networks.

Bilayer LDPC Codes for the Relay Channel

This paper describes a methodology for efficient implementation of binning and block-Markov coding for the relay channel using powerful features of low-density parity-check (LDPC) codes. We devise bilayer LDPC codes to approach the theoretically promised rate of the decode-and-forward relaying strategy by incorporating relay-generated random linear paritybits in a specially designed bilayer graphical code structure. Bilayer density evolution is devised as a novel extension of the standard density evolution algorithm to analyze the performance of the proposed bilayer LDPC code. Based on this bilayer density evolution technique, an EXIT-chart-based code design method using linear programming is developed. While conventional LDPC codes are sensitively tuned to operate efficiently at a certain channel parameter, the proposed bilayer LDPC code is capable of working at two different channel parameters, the signal-to-noise ratio (SNR) at the relay and the SNR at the destination. In this paper, for specific channel parameters, it is demonstrated that a bilayer LDPC code can approach the theoretical decode-and-forward rate of the relay channel within a 0.19 dB gap to the source-relay channel capacity and a 0.34 dB gap to the relay-destination channel capacity.

Parity Forwarding for Multiple-Relay Networks

This paper proposes a relaying strategy for the multiple-relay network in which each relay decodes a selection of transmitted messages by other transmitting terminals, and forwards parities of the decoded codewords. This protocol improves the previously known achievable rate of the decode-and-forward (DF) strategy for multirelay networks by allowing relays to decode only a selection of messages from relays with strong links to it. Hence, each relay may have several choices as to which messages to decode, and for a given network many different parity forwarding protocols may exist. A tree structure is devised to characterize a class of parity forwarding protocols for an arbitrary multirelay network. Based on this tree structure, closed-form expressions for the achievable rates of these DF schemes are derived. It is shown that parity forwarding is capacity achieving for new forms of degraded relay networks.

Universal relaying for the interference channel

This paper considers a Gaussian relay-interference channel and introduces a generalized hash-and-forward relay strategy, where the relay sends out a bin index of its quantized observation, and the receivers first decode the relay quantization codeword to a list, then use the list to help decode the respective messages from the transmitters. The main advantage of the proposed approach is in a scenario where the relay observes a linear combination of the transmitted signals and broadcasts a common relay message through a digital relay link of fixed rate to help both receivers of the interference channel. We show that when compared to the achievable rates with interference treated as noise, generalized hash-and-forward can provide one bit of rate improvement for every relay bit for both users at the same time in an asymptotic regime where the background noises go down to zero. The proposed approach is universal, in contrast to the compress-and-forward or amplify-and-forward strategies which are not asymptotically optimal for multiple users simultaneously, if at all.

Bit-Interleaved Coded Modulation for the Relay Channel Using Bilayer LDPC Codes

This paper describes a coding scheme for approaching the maximum theoretical decode-and-forward rate for the relay channel in the high signal-to-noise ratio (SNR) regime. The proposed scheme is based on a concatenation of bit-interleaved coded modulation (BICM) and a specially designed bilayer low-density parity-check (BLDPC) code that works simultaneously at two different SNRs. It is shown that the proposed BICM-BLDPC scheme provides a close-to-optimal performance for the relay channel at high SNRs, with a gap of 0.5 dB to the theoretical limit, at a bit error rate of 10-1.

Two Birds and One Stone: Gaussian Interference Channel With a Shared Out-of-Band Relay of Limited Rate

The two-user Gaussian interference channel with a shared out-of-band relay is considered. The relay observes a linear combination of the source signals and broadcasts a common message to the two destinations, through a perfect link of fixed limited rate R0 bits per channel use. The out-of-band nature of the relay is reflected by the fact that the common relay message does not interfere with the received signal at the two destinations. A general achievable rate is established, along with upper bounds on the capacity region for the Gaussian case. For R0 values below a certain threshold, which depends on channel parameters, in achievable rates asymptotically in regimes where joint a two-for-one gain is achievable by the capacity region of this channel is determined in this paper to within a constant gap of Δ = 1.95 bits. We identify interference regimes where a two-for-one gain in achievable rates is possible for every bit relayed, up to a constant approximation error. Instrumental to these results is a carefully designed quantize-and-forward type of relay strategy along with a joint decoding scheme employed at destination ends. Further, we also study successive decoding strategies with optimal decoding order (corresponding to the order at which common, private, and relay messages are decoded), and identify interference regimes where with an optimal decoding order, successive decoding may also achieve two-for-one gains similar to joint decoding; yet, in general, successive decoding produces unbounded loss asymptotically when compared to joint decoding.

A nonlinear approach to interference alignment

Cadambe and Jafar (CJ) alignment strategy for the K-user scalar frequency-selective fading Gaussian channel, with encoding over blocks of 2n+1 random channel coefficients (subcarriers) is considered. The linear zero-forcing (LZF) strategy is compared with a novel approach based on lattice alignment and lattice decoding (LD). Despite both LZF and LD achieve the same degrees of freedom, it is shown that LD can achieve very significant improvements in terms of error rates at practical SNRs with respect to the conventional LZF proposed in the literature. We also show that these gains are realized provided that channel gains are controlled to be near constant, for example, by means of power control and opportunistic carrier and user selection strategies. In presence of relatively-small variations in the normalized channel coefficient amplitudes, CJ alignment strategy yields very disappointing results at finite SNRs, and the gain of LD over ZLF significantly reduces. In light of these results, the practical applicability of CJ alignment scheme remains questionable, in particular for Rayleigh fading channels, where channel inversion power control yields to unbounded average transmit power.

Interference alignment, carrier pairing, and lattice decoding

We discuss how to take advantage of the discreteness of signal constellations at the detector side, in various interference alignment schemes for which linear zero-forcing of the interference has been traditionally considered. We show that lattice decoding, with possible “generalized decision feedback equalization” preprocessing can achieve significant gains in symbol error rate at the detector output, at finite SNR. Furthermore, we discuss the effect of channel coefficient dynamics on the Cadambe and Jafar interference alignment precoding scheme, and point out the need of careful carrier pairing in order to limit these dynamics.