3 research outputs found
First-Passage Time and Large-Deviation Analysis for Erasure Channels with Memory
This article considers the performance of digital communication systems
transmitting messages over finite-state erasure channels with memory.
Information bits are protected from channel erasures using error-correcting
codes; successful receptions of codewords are acknowledged at the source
through instantaneous feedback. The primary focus of this research is on
delay-sensitive applications, codes with finite block lengths and, necessarily,
non-vanishing probabilities of decoding failure. The contribution of this
article is twofold. A methodology to compute the distribution of the time
required to empty a buffer is introduced. Based on this distribution, the mean
hitting time to an empty queue and delay-violation probabilities for specific
thresholds can be computed explicitly. The proposed techniques apply to
situations where the transmit buffer contains a predetermined number of
information bits at the onset of the data transfer. Furthermore, as additional
performance criteria, large deviation principles are obtained for the empirical
mean service time and the average packet-transmission time associated with the
communication process. This rigorous framework yields a pragmatic methodology
to select code rate and block length for the communication unit as functions of
the service requirements. Examples motivated by practical systems are provided
to further illustrate the applicability of these techniques.Comment: To appear in IEEE Transactions on Information Theor
Capacity-Achieving Coding Mechanisms: Spatial Coupling and Group Symmetries
The broad theme of this work is in constructing optimal transmission mechanisms for a wide variety of communication systems. In particular, this dissertation provides a proof of threshold saturation for spatially-coupled codes, low-complexity capacity-achieving coding schemes for side-information problems, a proof that Reed-Muller and primitive narrow-sense BCH codes achieve capacity on erasure channels, and a mathematical framework to design delay sensitive communication systems.
Spatially-coupled codes are a class of codes on graphs that are shown to achieve capacity universally over binary symmetric memoryless channels (BMS) under belief-propagation decoder. The underlying phenomenon behind spatial coupling, known as âthreshold saturation via spatial couplingâ, turns out to be general and this technique has been applied to a wide variety of systems. In this work, a proof of the threshold saturation phenomenon is provided for irregular low-density parity-check (LDPC) and low-density generator-matrix (LDGM) ensembles on BMS channels. This proof is far simpler than published alternative proofs and it remains as the only technique to handle irregular and LDGM codes. Also, low-complexity capacity-achieving codes are constructed for three coding problems via spatial coupling: 1) rate distortion with side-information, 2) channel coding with side-information, and 3) write-once memory system. All these schemes are based on spatially coupling compound LDGM/LDPC ensembles.
Reed-Muller and Bose-Chaudhuri-Hocquengham (BCH) are well-known algebraic codes introduced more than 50 years ago. While these codes are studied extensively in the literature it wasnât known whether these codes achieve capacity. This work introduces a technique to show that Reed-Muller and primitive narrow-sense BCH codes achieve capacity on erasure channels under maximum a posteriori (MAP) decoding. Instead of relying on the weight enumerators or other precise details of these codes, this technique requires that these codes have highly symmetric permutation groups. In fact, any sequence of linear codes with increasing blocklengths whose rates converge to a number between 0 and 1, and whose permutation groups are doubly transitive achieve capacity on erasure channels under bit-MAP decoding. This pro-vides a rare example in information theory where symmetry alone is suïŹcient to achieve capacity.
While the channel capacity provides a useful benchmark for practical design, communication systems of the day also demand small latency and other link layer metrics. Such delay sensitive communication systems are studied in this work, where a mathematical framework is developed to provide insights into the optimal design of these systems