We focus on full-rate, fast-decodable space-time block codes (STBCs) for 2x2 and 4x2 multiple-input multiple-output (MIMO) transmission. We first derive conditions for reduced-complexity maximum-likelihood decoding, and apply them to a unified analysis of two families of 2x2 STBCs that were recently proposed. In particular, we describe a reduced-complexity sphere decoding algorithm suitable for QAM signal constellations. Next, we derive a novel reduced-complexity 4x2 STBC, and show that it outperforms all previously known codes with certain constellations.
Let $K/F$ and $K/L$ be two cyclic Galois field extensions and $D=(K/F,σ,c)$ a cyclic algebra. Given an invertible element $d\in D$, we present three families of unital nonassociative algebras over $L\cap F$ defined on the direct sum of $n$ copies of $D$. Two of these families appear either explicitly or implicitly in the designs of fast-decodable space-time block codes in papers by Srinath, Rajan, Markin, Oggier, and the authors. We present conditions for the algebras to be division and propose a construction for fully diverse fast decodable space-time block codes of rate-$m$ for $nm$ transmit…
Fast-decodable distributed space-time codes are constructed by adapting the iterative code construction introduced in [1] to the N -relay multiple-input multiple-output channel, leading to the first fast-decodable distributed space-time codes for more than one antenna per user. Explicit constructions are provided alongside with a performance comparison to non-iterated (non-) fast-decodable codes.
In this paper, we present an explicit construction of list-decodable codes for single-deletion and single-substitution with list size two and redundancy 3log n+4, where n is the block length of the code. Our construction has lower redundancy than the best known explicit construction by Gabrys et al. (arXiv 2021), whose redundancy is 4log n+O(1).
In this paper, we propose a fast decoder algorithm for uniquely decodable (errorless) code sets for overloaded synchronous optical code-division multiple-access (O-CDMA) systems. The proposed decoder is designed in a such a way that the users can uniquely recover the information bits with a very simple decoder, which uses only a few comparisons. Compared to maximum-likelihood (ML) decoder, which has a high computational complexity for even moderate code lengths, the proposed decoder has much lower computational complexity. Simulation results in terms of bit error rate (BER) demonstrate that th…
In this article, the first general constructions of fast-decodable, more specifically (conditionally) $g$-group decodable, space-time block codes for the Nonorthogonal Amplify and Forward (NAF) Multiple-Input Multiple-Output (MIMO) relay channel under the half-duplex constraint are proposed. In this scenario, the source and the intermediate relays used for data amplification are allowed to employ multiple antennas for data transmission and reception. The worst-case decoding complexity of the obtained codes is reduced by up to $75%$. In addition to being fast-decodable, the proposed codes achie…
We construct locally decodable codes (LDCs) to correct insertion-deletion errors in the setting where the sender and receiver share a secret key or where the channel is resource-bounded. Our constructions rely on a so-called "Hamming-to-InsDel" compiler (Ostrovsky and Paskin-Cherniavsky, ITS '15 & Block et al., FSTTCS '20), which compiles any locally decodable Hamming code into a locally decodable code resilient to insertion-deletion (InsDel) errors. While the compilers were designed for the classical coding setting, we show that the compilers still work in a secret key or resource-bounded set…
In the near future, the $5^{th}$ generation (5G) wireless systems will be established. They will consist of an integration of different techniques, including distributed antenna systems and massive multiple-input multiple-output systems, and the overall performance will highly depend on the channel coding techniques employed. Due to the nature of future wireless networks, space--time codes are no longer merely an object of choice, but will often appear naturally in the communications setting. However, as the involved communication devices often exhibit a modest computational power, the complex…
A locally decodable code (LDC) C:{0,1}^k -> {0,1}^n is an error correcting code wherein individual bits of the message can be recovered by only querying a few bits of a noisy codeword. LDCs found a myriad of applications both in theory and in practice, ranging from probabilistically checkable proofs to distributed storage. However, despite nearly two decades of extensive study, the best known constructions of O(1)-query LDCs have super-polynomial blocklength. The notion of relaxed LDCs is a natural relaxation of LDCs, which aims to bypass the foregoing barrier by requiring local decoding of ne…
In this work, we give the first construction of high-rate locally list-recoverable codes. List-recovery has been an extremely useful building block in coding theory, and our motivation is to use these codes as such a building block. In particular, our construction gives the first capacity-achieving locally list-decodable codes (over constant-sized alphabet); the first capacity achieving globally list-decodable codes with nearly linear time list decoding algorithm (once more, over constant-sized alphabet); and a randomized construction of binary codes on the Gilbert-Varshamov bound that can be …
The design of linear STBCs offering a low-complexity ML decoding using the well known Sphere Decoder (SD) has been extensively studied in last years. The first considered approach to derive design criteria for the construction of such codes is based on the Hurwitz-Radon (HR) Theory for mutual orthogonality between the weight matrices defining the linear code. This appproach served to construct new families of codes admitting fast sphere decoding such as multi-group decodable, fast decodable, and fast-group decodable codes. In a second Quadratic Form approach, the Fast Sphere Decoding (FSD) com…
Fountain codes are erasure correcting codes realizing reliable communication systems for the multicast on the Internet. The zigzag decodable fountain (ZDF) code is one of generalization of the Raptor code, i.e, applying shift operation to generate the output packets. The ZDF code is decoded by a two-stage iterative decoding algorithm, which combines the packet-wise peeling algorithm and the bit-wise peeling algorithm. By the bit-wise peeling algorithm and shift operation, ZDF codes outperform Raptor codes under iterative decoding in terms of decoding erasure rate and overhead. However, the bit…
Recent efforts in coding theory have focused on building codes for insertions and deletions, called insdel codes, with optimal trade-offs between their redundancy and their error-correction capabilities, as well as efficient encoding and decoding algorithms. In many applications, polynomial running time may still be prohibitively expensive, which has motivated the study of codes with super-efficient decoding algorithms. These have led to the well-studied notions of Locally Decodable Codes (LDCs) and Locally Correctable Codes (LCCs). Inspired by these notions, Ostrovsky and Paskin-Cherniavsky (…
In this paper, we consider the so-called uniquely decodable one-to-one code (UDOOC) that is formed by inserting a "comma" indicator, termed the unique word (UW), between consecutive one-to-one codewords for separation. Along this research direction, we first investigate several general combinatorial properties of UDOOCs, in particular the enumeration of the number of UDOOC codewords for any (finite) codeword length. Based on the obtained formula on the number of length-n codewords for a given UW, the per-letter average codeword length of UDOOC for the optimal compression of a given source stat…
Fast-Decodable Asymmetric Space-Time Codes from Division Algebras
多输入双输出（MIDO）码在不久的将来的无线通信中是重要的，其中便携式终端用户设备物理上很小并且通常将包含至多两个接收天线。特别诱人的是4 x 2通道，由于其在数字视频广播（DVB）中的直接适用性。这种信道最佳地采用由（4 × 4）矩阵组成的速率2空时（ST）码。不幸的是，这样的代码通常解码起来非常复杂，因此提出了对具有降低的复杂性的构造的要求。最近，已经提出了一些降低复杂性的结构，但它们主要是基于不同的特设方法，并导致孤立的例子，而不是在一个更一般的代码类。在本文中，它将被证明，一个家庭的划分代数为基础的MIDO码将始终导致至少37.5%的最坏情况下的复杂性降低，同时保持充分的多样性，并首次，非零行列式（NVD）属性。减少遵循的事实是，类似于阿拉姆码，代码将是哈密尔顿四元数的矩阵环的子集，因此允许简化解码。目前，这种减少是最有名的速率二MIDO码。通过计算机模拟，给出了几种显式结构，并证明了它们具有优良的性能。
Grant-free multiple-access (GFMA) is a valuable research topic, since it can support multiuser transmission with low latency. This paper constructs novel uniquely-decodable multi-amplitude sequence (UDAS) sets for GFMA systems, which can provide high spectrum efficiency (SE) with low-complexity active user detection (AUD) algorithm. First of all, we propose an UDAS-based multi-dimensional bit interleaving coded modulation (MD-BICM) transmitter; then introduce the definition of UDAS and construct two kinds of UDAS sets based on cyclic and quasi-cyclic matrix modes. Besides, we present a statist…
Arikan's Polar codes attracted much attention as the first efficiently decodable and capacity achieving codes. Furthermore, Polar codes exhibit an exponentially decreasing block error probability with an asymptotic error exponent upper bounded by 1/2. Since their discovery, many attempts have been made to improve the error exponent and the finite block-length performance, while keeping the bloc-structured kernel. Recently, two of us introduced a new family of efficiently decodable error-correction codes based on a recently discovered efficiently-contractible tensor network family in quantum ma…
