{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:47:32Z","timestamp":1760240852962,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,9,29]],"date-time":"2019-09-29T00:00:00Z","timestamp":1569715200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Lattices provide useful structure for distributed coding of correlated sources. A common lattice encoder construction is to first round an observed sequence to a \u2018fine\u2019 lattice with dither, then produce the result\u2019s modulo to a \u2018coarse\u2019 lattice as the encoding. However, such encodings may be jointly-dependent. A class of upper bounds is established on the conditional entropy-rates of such encodings when sources are correlated and Gaussian and the lattices involved are a from an asymptotically-well-behaved sequence. These upper bounds guarantee existence of a joint\u2013compression stage which can increase encoder efficiency. The bounds exploit the property that the amount of possible values for one encoding collapses when conditioned on other sufficiently informative encodings. The bounds are applied to the scenario of communicating through a many-help-one network in the presence of strong correlated Gaussian interferers, and such a joint\u2013compression stage is seen to compensate for some of the inefficiency in certain simple encoder designs.<\/jats:p>","DOI":"10.3390\/e21100957","type":"journal-article","created":{"date-parts":[[2019,9,30]],"date-time":"2019-09-30T05:58:33Z","timestamp":1569823113000},"page":"957","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Upper Bound on the Joint Entropy of Correlated Sources Encoded by Good Lattices"],"prefix":"10.3390","volume":"21","author":[{"given":"Christian","family":"Chapman","sequence":"first","affiliation":[{"name":"School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85281, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel W.","family":"Bliss","sequence":"additional","affiliation":[{"name":"School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85281, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zamir, R. (2014). Lattice Coding for Signals and Networks: A Structured Coding Approach to Quantization, Modulation, and Multiuser Information Theory, Cambridge University Press.","DOI":"10.1017\/CBO9781139045520"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4439","DOI":"10.1109\/TIT.2016.2571719","article-title":"A simple proof for the existence of \u201cgood\u201d pairs of nested lattices","volume":"62","author":"Ordentlich","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Chapman, C., Kinsinger, M., Agaskar, A., and Bliss, D.W. (2019). Distributed Recovery of a Gaussian Source in Interference with Successive Lattice Processing. Entropy, 21.","DOI":"10.3390\/e21090845"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TIT.2004.834787","article-title":"Achieving 12log(1+SNR) on the AWGN Channel With Lattice Encoding and Decoding","volume":"50","author":"Erez","year":"2004","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ordentlich, O., Erez, U., and Nazer, B. (2013, January 2\u20134). Successive integer-forcing and its sum-rate optimality. Proceedings of the 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton), Monticello, IL, USA.","DOI":"10.1109\/Allerton.2013.6736536"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1109\/TIT.2014.2370047","article-title":"Precoded integer-forcing universally achieves the MIMO capacity to within a constant gap","volume":"61","author":"Ordentlich","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1109\/TIT.2010.2090225","article-title":"On Distributed Compression of Linear Functions","volume":"57","author":"Wagner","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Yang, Y., and Xiong, Z. (2011, January 6\u201311). An improved lattice-based scheme for lossy distributed compression of linear functions. Proceedings of the 2011 Information Theory and Applications Workshop, La Jolla, CA, USA.","DOI":"10.1109\/ITA.2011.5743626"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2835","DOI":"10.1109\/TIT.2014.2311809","article-title":"Distributed compression of linear functions: Partial sum-rate tightness and gap to optimal sum-rate","volume":"60","author":"Yang","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1109\/TIT.2018.2864638","article-title":"Generalized compute-compress-and-forward","volume":"65","author":"Cheng","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_11","first-page":"564","article-title":"The Gaussian Many-help-one Distributed Source Coding Problem","volume":"56","author":"Saurabha","year":"2009","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3008","DOI":"10.1109\/TIT.2008.924659","article-title":"Communication via Decentralized Processing","volume":"54","author":"Sanderovich","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Chapman, C.D., Mittelmann, H., Margetts, A.R., and Bliss, D.W. (2018). A Decentralized Receiver in Gaussian Interference. Entropy, 20.","DOI":"10.3390\/e20040269"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"El Gamal, A., and Kim, Y.H. (2011). Network Information Theory, Cambridge University Press.","DOI":"10.1017\/CBO9781139030687"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/BF01581144","article-title":"Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems","volume":"66","author":"Schnorr","year":"1994","journal-title":"Math. Program."},{"key":"ref_16","unstructured":"Buchmann, J., and Pohst, M. (1987, January 2\u20135). Computing a Lattice Basis from a System of Generating Vectors. Proceedings of the European Conference on Computer Algebra, Leipzig, Germany."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1137\/0218059","article-title":"Polynomial time algorithms for finding integer relations among real numbers","volume":"18","author":"Hastad","year":"1989","journal-title":"SIAM J. Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3530","DOI":"10.1109\/TIT.2011.2143830","article-title":"Faster recursions in sphere decoding","volume":"57","author":"Ghasemmehdi","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Krithivasan, D., and Pradhan, S.S. (2007). Lattices for Distributed Source Coding: Jointly Gaussian Sources and Reconstruction of a Linear Function. International Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, Springer.","DOI":"10.1007\/978-3-540-77224-8_22"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3401","DOI":"10.1109\/TIT.2005.855591","article-title":"Lattices Which are Good for (Almost) Everything","volume":"51","author":"Erez","year":"2005","journal-title":"IEEE Trans. Inf. 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