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In this paper, we study the list decoding error probability of a linear code over the erasure channel. The notion of L-incorrigible sets of a linear code is introduced to characterize its performance under list decoding. The L-incorrigible set distribution of a linear code can also be used to completely determine its decoding error probability under maximum likelihood decoding over the erasure channel...
Gabidulin codes can be seen as the rank-metric equivalent of Reed-Solomon codes. It was recently proven, using subspace polynomials, that Gabidulin codes cannot be list decoded beyond the so-called Johnson radius. In another result, cyclic subspace codes were constructed by inspecting the connection between subspaces and their subspace polynomials. In this paper, these subspace codes are used to prove...
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate R ∈ [0, 1]. An efficient interpolation-based decoding algorithm for this code construction is given which allows to correct insertions and deletions up to the normalized radius s (1 − ((1/h + h)/(h − s + 1))R), where h...
An interpolation-based list decoding algorithm for ℓ-quasi-cyclic codes over finite fields is developed and its guaranteed decoding radius for ℓ-phased burst errors is proven. It is also shown that for this error model and for certain parameter ranges, this new approach is advantageous over existing schemes.
Motivated by the cellular uplink scenario along with the increasing capabilities of radio nodes, we consider a state-dependent multiple-access channel in which the encoders can overhear other transmissions while simultaneously sending their own transmissions. In addition, the channel is state dependent and encoders have access to independent causal state information while the decoder has complete...
In this paper we study the cooperative multiple access channel (MAC) with oblivious encoders and characterize its capacity region. Cooperation means that one encoder sends a message to the other encoder via a rate-limited link prior to transmission, while partial cribbing means that one encoder obtains a deterministic function of the other encoder's output. Partial cribbing can be done strictly-causally,...
We consider a multiple access communication system where multiple users share a common collision channel. In this system, coordination among users is essential to resolve collision issues. However, each system user can only observe its own local traffic and the feedback from the channel. Without a centralized controller, it is challenging to design an efficient coordination protocol. We present a...
In cooperative communication, network nodes that would otherwise act independently instead coordinate their efforts with the aim of improving communication performance. To better understand cooperation, we consider communication over a multiple access channel using a “cooperation facilitator”, a node that receives rate-limited message descriptions from the transmitters and sends rate-limited message...
Spatially-coupled regular LDPC code ensembles have outstanding performance with belief propagation decoding and can perform arbitrarily close to the Shannon limit without requiring irregular graph structures. In this paper, we are concerned with the performance and complexity of spatially-coupled ensembles with a rate-compatibility constraint. Spatially-coupled regular ensembles that support rate-compatibility...
This paper proposes two new cycle-optimized algorithms, called the multi-step progressive edge-growth (PEG) algorithm and the multi-step approximate cycle extrinsic message degree (ACE) constrained PEG algorithm, to design an LDPC code with larger girth and better cycle-connectivity. In addition, an efficient method is developed to calculate the distances between the variable nodes (VNs) and the check...
In the infinite blocklength regime, spatially-coupled LDPC codes are capable of achieving capacity-approaching performance under message-passing decoding. In the finite blocklength regime, it is known that absorbing sets compete with the codewords to be the output of sub-optimal message-passing decoders: the existence of such sets in the Tanner graph of LDPC codes causes performance degradation in...
We analyze a class of high performance, low decoding data-flow codes suitable for high bit-rate optical-fiber communication systems. A spatially-coupled split-component ensemble is defined, encompassing the most representative codes in this class, staircase codes and braided block codes. Our definition preserves two important properties of this class of codes: deterministic partitioning of component-code...
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