The price of certainty: "waterslide curves" and the gap to capacity

The classical problem of reliable point-to-point digital communication is to achieve a low probability of error while keeping the rate high and the total power consumption small. Traditional information-theoretic analysis uses `waterfall' curves to convey the revolutionary idea that unboundedly low probabilities of bit-error are attainable using only finite transmit power. However, practitioners have long observed that the decoder complexity, and hence the total power consumption, goes up when attempting to use sophisticated codes that operate close to the waterfall curve. This paper gives an explicit model for power consumption at an idealized decoder that allows for extreme parallelism in implementation. The decoder architecture is in the spirit of message passing and iterative decoding for sparse-graph codes. Generalized sphere-packing arguments are used to derive lower bounds on the decoding power needed for any possible code given only the gap from the Shannon limit and the desired probability of error. As the gap goes to zero, the energy per bit spent in decoding is shown to go to infinity. This suggests that to optimize total power, the transmitter should operate at a power that is strictly above the minimum demanded by the Shannon capacity. The lower bound is plotted to show an unavoidable tradeoff between the average bit-error probability and the total power used in transmission and decoding. In the spirit of conventional waterfall curves, we call these `waterslide' curves.Comment: 37 pages, 13 figures. Submitted to IEEE Transactions on Information Theory. This version corrects a subtle bug in the proofs of the original submission and improves the bounds significantl

Modified VLSI designs for error correction codes

Nowadays, error correction codes have become an integral part in almost all the modern digital communication and storage systems. With the continuously increasing demands for higher speed and lower power communication systems, efficient VLSI implementations of those error correction codes have great importance for practical applications. In this thesis, several VLSI design issues for Viterbi decoder and Low-Density Parity-Check (LDPC) codes decoder will be discussed. We propose a low-power memory-efficient Viterbi decoder to reduce the memory read operations in the survivor memory unit (SMU) and the memory size of SMU. We develop a parallel Viterbi decoder for high throughput applications. We also propose an efficient early stopping scheme to reduce the number of decoding iterations for LDPC codes decoding

Efficient Transmission Techniques in Cooperative Networks: Forwarding Strategies and Distributed Coding Schemes

This dissertation focuses on transmission and estimation schemes in wireless relay network, which involves a set of source nodes, a set of destination nodes, and a set of nodes helps communication between source nodes and destination nodes, called relay nodes. It is noted that the overall performance of the wireless relay systems would be impacted by the relay methods adopted by relay nodes. In this dissertation, efficient forwarding strategies and channel coding involved relaying schemes in various relay network topology are studied.First we study a simple structure of relay systems, with one source, one destination and one relay node. By exploiting “analog codes” -- a special class of error correction codes that can directly encode and protect real-valued data, a soft forwarding strategy –“analog-encode-forward (AEF)”scheme is proposed. The relay node first soft-decodes the packet from the source, then re-encodes this soft decoder output (Log Likelihood Ratio) using an appropriate analog code, and forwards it to the destination. At the receiver, both a maximum-likelihood (ML) decoder and a maximum a posterior (MAP) decoder are specially designed for the AEF scheme.The work is then extended to parallel relay networks, which is consisted of one source, one destination and multiple relay nodes. The first question confronted with us is which kind of soft information to be relayed at the relay nodes. We analyze a set of prevailing soft information for relaying considered by researchers in this field. A truncated LLR is proved to be the best choice, we thus derive another soft forwarding strategy – “Z” forwarding strategy. The main parameter effecting the overall performance in this scheme is the threshold selected to cut the LLR information. We analyze the threshold selection at the relay nodes, and derive the exact ML estimation at the destination node. To circumvent the catastrophic error propagation in digital distributed coding scheme, a distributed soft coding scheme is proposed for the parallel relay networks. The key idea is the exploitation of a rate-1 soft convolutional encoder at each of the parallel relays, to collaboratively form a simple but powerful distributed analog coding scheme. Because of the linearity of the truncated LLR information, a nearly optimal ML decoder is derived for the distributed coding scheme. In the last part, a cooperative transmission scheme for a multi-source single-destination system through superposition modulation is investigated. The source nodes take turns to transmit, and each time, a source “overlays” its new data together with (some or all of) what it overhears from its partner(s), in a way similar to French-braiding the hair. We introduce two subclasses of braid coding, the nonregenerative and the regenerative cases, and, using the pairwise error probability (PEP) as a figure of merit, derive the optimal weight parameters for each one. By exploiting the structure relevance of braid codes with trellis codes, we propose a Viterbi maximum-likelihood (ML) decoding method of linear-complexity for the regenerative case. We also present a soft-iterative joint channel-network decoding. The overall decoding process is divided into the forward message passing and the backward message passing, which makes effective use of the available reliability information from all the received signals. We show that the proposed “braid coding” cooperative scheme benefits not only from the cooperative diversity but also from the bit error rate (BER) performance gain

Software and hardware implementation techniques for digital communications-related algorithms

There are essentially three areas addressed in the body of this thesis. (a) The first is a theoretical investigation into the design and development of a practically realizable implementation of a maximum-likelihood detection process to deal with digital data transmission over HF radio links. These links exhibit multipath properties with delay spreads that can easily extend over 12 to 15 milliseconds. The project was sponsored by the Ministry of Defence through the auspices of the Science and Engineering Research Council. The primary objective was to transmit voice band data at a minimum rate of 2.4 kb/s continuously for long periods of time during the day or night. Computer simulation models of HF propagation channels were created to simulate atmospheric and multipath effects of transmission from London to Washington DC, Ankara, and as far as Melbourne, Australia. Investigations into HF channel estimation are not the subject of this thesis. The detection process assumed accurate knowledge of the channel. [Continues.