High-Throughput Random Access via Codes on Graphs

Recently, contention resolution diversity slotted ALOHA (CRDSA) has been introduced as a simple but effective improvement to slotted ALOHA. It relies on MAC burst repetitions and on interference cancellation to increase the normalized throughput of a classic slotted ALOHA access scheme. CRDSA allows achieving a larger throughput than slotted ALOHA, at the price of an increased average transmitted power. A way to trade-off the increment of the average transmitted power and the improvement of the throughput is presented in this paper. Specifically, it is proposed to divide each MAC burst in k sub-bursts, and to encode them via a (n,k) erasure correcting code. The n encoded sub-bursts are transmitted over the MAC channel, according to specific time/frequency-hopping patterns. Whenever n-e>=k sub-bursts (of the same burst) are received without collisions, erasure decoding allows recovering the remaining e sub-bursts (which were lost due to collisions). An interference cancellation process can then take place, removing in e slots the interference caused by the e recovered sub-bursts, possibly allowing the correct decoding of sub-bursts related to other bursts. The process is thus iterated as for the CRDSA case.Comment: Presented at the Future Network and MobileSummit 2010 Conference, Florence (Italy), June 201

Coded Slotted ALOHA: A Graph-Based Method for Uncoordinated Multiple Access

In this paper, a random access scheme is introduced which relies on the combination of packet erasure correcting codes and successive interference cancellation (SIC). The scheme is named coded slotted ALOHA. A bipartite graph representation of the SIC process, resembling iterative decoding of generalized low-density parity-check codes over the erasure channel, is exploited to optimize the selection probabilities of the component erasure correcting codes via density evolution analysis. The capacity (in packets per slot) of the scheme is then analyzed in the context of the collision channel without feedback. Moreover, a capacity bound is developed and component code distributions tightly approaching the bound are derived.Comment: The final version to appear in IEEE Trans. Inf. Theory. 18 pages, 10 figure

Ningyō Sashichi and Hanshichi: Differing Views on Ancient Edo

Torimonochō have enjoyed immense popularity in Japan since their inception: through highs and lows, these stories have managed to survive for a hundred years with little to no interruption, even during the bleak days of the Pacific War. Even now, when this literary genre has fallen under the radar, and many among the younger generations are unfamiliar with it, it still enjoys a moderate degree of success in its niche market, and it is an important part of the Japanese literary landscape. Despite the depth of the roots torimonochō have in Japan, scholarly attention towards the genre has not been forthcoming: literary criticism in Japanese is not plentiful, and tends to concentrate on a single series, Hanshichi torimonochō, to the near exclusion of others, and the situation is further exacerbated by the extreme scarcity of translations. The present work aims to bridge this gap, however partially, not just by introducing torimonochō to a Western audience, but by presenting some of its lesser-known aspects, and arguing for a re-evaluation of the genre itself. Torimonochō are often presented, and present in the public mind, as an unambiguous unit, something of a monolithic block with little in the way of change: detective stories set in a nostalgia-fuelled Edo period – a ‘golden age’, or the ‘good old times’ – with very rigid, well-defined characteristics more or less impervious to modifications. On a closer look, however, within the compact and apparently strict definition of ‘torimonochō’, one finds a much more fragmentary reality, an amalgamation of different elements which do not even necessarily mesh well with each other. Torimonochō are not a single block, then, but a construction made of many smaller ‘bricks’, quite varied and rarely homogeneous. A hybrid mass without substantial unity, in other words, a commixture the characteristics of which change depending on the author’s vision – and even the reader’s vision. This hybridity manifests itself in three different stages, or layers: (a) the origins of the torimonochō, how they came about and reached their present form; (b) its representational content, how they depict the fantasy world the protagonists inhabit and what this depiction tells us about the real world the authors lived in; and (c) their surrounding context, how the external circumstances around the times of their publication variously affected not just single works, but genre definitions themselves. These three forms of hybridity will be the main subject of the present thesis, the four chapters of which will explore each of these individual sides with the intention of demonstrating that torimonochō is a fundamentally inhomogeneous literary genre. Given the plethora of works, the scope of the paper is limited to the so-called ‘Five Great Torimonochō’: Umon torimonochō, Zenigata Heiji torimono hikae, Wakasama zamurai torimono techō, Hanshichi torimonochō, and Ningyō Sashichi torimonochō, with a special focus on the latter two. The Hanshichi series is of capital importance, not just because it gave birth to the genre itself, but also for its curious ‘heretical’ status among its epigones. The Sashichi series, on the other hand, introduces many variations which set it starkly apart from the traditional concept of torimonochō, endowing it with an importance which has not always been acknowledged by critics

Minimum Distance Distribution of Irregular Generalized LDPC Code Ensembles

In this paper, the minimum distance distribution of irregular generalized LDPC (GLDPC) code ensembles is investigated. Two classes of GLDPC code ensembles are analyzed; in one case, the Tanner graph is regular from the variable node perspective, and in the other case the Tanner graph is completely unstructured and irregular. In particular, for the former ensemble class we determine exactly which ensembles have minimum distance growing linearly with the block length with probability approaching unity with increasing block length. This work extends previous results concerning LDPC and regular GLDPC codes to the case where a hybrid mixture of check node types is used.Comment: 5 pages, 1 figure. Submitted to the IEEE International Symposium on Information Theory (ISIT) 201

A Decoding Algorithm for LDPC Codes Over Erasure Channels with Sporadic Errors

none4An efficient decoding algorithm for low-density parity-check (LDPC) codes on erasure channels with sporadic errors (i.e., binary error-and-erasure channels with error probability much smaller than the erasure probability) is proposed and its performance analyzed. A general single-error multiple-erasure (SEME) decoding algorithm is first described, which may be in principle used with any binary linear block code. The algorithm is optimum whenever the non-erased part of the received word is affected by at most one error, and is capable of performing error detection of multiple errors. An upper bound on the average block error probability under SEME decoding is derived for the linear random code ensemble. The bound is tight and easy to implement. The algorithm is then adapted to LDPC codes, resulting in a simple modification to a previously proposed efficient maximum likelihood LDPC erasure decoder which exploits the parity-check matrix sparseness. Numerical results reveal that LDPC codes under efficient SEME decoding can closely approach the average performance of random codes.noneG. Liva; E. Paolini; B. Matuz; M. ChianiG. Liva; E. Paolini; B. Matuz; M. Chian

Spatially-Coupled Random Access on Graphs

In this paper we investigate the effect of spatial coupling applied to the recently-proposed coded slotted ALOHA (CSA) random access protocol. Thanks to the bridge between the graphical model describing the iterative interference cancelation process of CSA over the random access frame and the erasure recovery process of low-density parity-check (LDPC) codes over the binary erasure channel (BEC), we propose an access protocol which is inspired by the convolutional LDPC code construction. The proposed protocol exploits the terminations of its graphical model to achieve the spatial coupling effect, attaining performance close to the theoretical limits of CSA. As for the convolutional LDPC code case, large iterative decoding thresholds are obtained by simply increasing the density of the graph. We show that the threshold saturation effect takes place by defining a suitable counterpart of the maximum-a-posteriori decoding threshold of spatially-coupled LDPC code ensembles. In the asymptotic setting, the proposed scheme allows sustaining a traffic close to 1 [packets/slot].Comment: To be presented at IEEE ISIT 2012, Bosto

Bounds on the Error Probability of Raptor Codes under Maximum Likelihood Decoding

In this paper upper and lower bounds on the probability of decoding failure under maximum likelihood decoding are derived for different (nonbinary) Raptor code constructions. In particular four different constructions are considered; (i) the standard Raptor code construction, (ii) a multi-edge type construction, (iii) a construction where the Raptor code is nonbinary but the generator matrix of the LT code has only binary entries, (iv) a combination of (ii) and (iii). The latter construction resembles the one employed by RaptorQ codes, which at the time of writing this article represents the state of the art in fountain codes. The bounds are shown to be tight, and provide an important aid for the design of Raptor codes.Comment: Submitted for revie